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Board for a frame house. Board for a frame house Frame houses have a number of advantages

Is it possible to cover a chessboard with 1x2 dominoes so that only cells a1 and h8 remain free?

Is it possible to cover a chessboard with a cut-out corner field with "corners"?

Mark several cells on the 8X8 board so that any (including any marked) cell borders exactly one marked cell on the side.

Can a 6X6 board with two opposite corners cut out be bypassed by a chess knight, visiting each cell exactly once?

Ilya was given a whole box with figurines in the form of a "pedestal" (see picture). a) Will he be able to tile an 8x8 chessboard with them? b) What about a 10X10 board?

There is a beetle in each square of the 5x5 board. At some point, all the beetles simultaneously crawl onto adjacent (horizontally or vertically) cells. Does this necessarily leave an empty cell?

Can the hexagonal cake (see picture) be cut into 23 equal pieces along the indicated lines?

Additional tasks 1.

The camel piece moves across the 10x10 board with a move like (1, 3) (that is, it moves first to an adjacent square, and then moves three more squares in a perpendicular direction; a knight, for example, moves like (1, 2)) . Is it possible to move the "camel" from some initial field to the adjacent one?

There are two black checkers diagonally on an endless chessboard. Is it possible to put a white checker and several black checkers on the board so that the white checker eats all the checkers on the board in one move?

Additional tasks 2.

Can a board of 10x10 cells be paved with tiles of 1x4 cells?

10. Is it possible to cover a chessboard with a cut-out corner field with identical rectangular "tiles" of size 1(3 cells?

11. A mouse nibbles on a cube of cheese made up of 27 single cubes. When she eats a cube, she moves to the next one through a common edge with the previous one. Can a mouse eat the whole cube except for the central cube?

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Can a 10x10 board be cut into pieces of four cells in the shape of the letter L? The castle has the shape of a regular triangle, divided into 49 halls, each of which also has the shape of a regular triangle (see picture). There is a door in the wall between any two halls. The traveler wants to go around as many halls as possible without going into any of them twice. What is the largest number of halls he will be able to bypass?

Building a frame house with your own hands is a process that is both complex and quite simple. We will analyze the sequence of actions during such construction, we will give as an example an approximate estimate for the construction of a 6x6 m house, including materials for the foundation, walls, roof and interfloor stairs. Based on such an approximate estimate, you will be able to independently draw up an individual project of a frame house, focusing on the required area and parameters of hotel elements and nodes.

The advantages of a frame house include its environmental safety, the possibility of rapid construction, reliability and durability.

The sequence of actions in the construction of a frame house

To build a 6x6 m frame house with your own hands, you must follow the following sequence of actions:

1. Prepare the site, apply markings for the future foundation.
2. For a frame house, a shallow strip foundation is excellent, for which a trench is dug around the perimeter, sand and gravel are poured to the bottom. Reinforcement and pouring of the tape is in progress.
3. Next, the frame of the floor of the first floor is constructed from edged boards, sheathed and insulated with mineral wool.
4. Wall frames can be made in 2 ways: assembled according to a template on a horizontal surface, then lifted and installed, or mounted directly on site, starting with the installation of racks, strapping, sewing.
5. The next step is to install the ceiling for the second floor, the ceiling frame in the same way.
6. Windows and door receptions are filled immediately, as the frame is built. The same applies to insulation, cladding and engineering networks. After the work is completed, it will be extremely difficult to conduct heating or an electrician.
7. Installation of truss system, battens, roof insulation.
8. Roofing material.

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Materials for the construction of a frame house

To put a frame house with your own hands, you must first calculate the materials that are needed for work. We offer an approximate estimate of materials for the construction of a small two-story house, which includes a complete list of everything you need.

The cost must be calculated based on the realities of today, since the price of building materials may change.

1. Foundation. In this case, a conventional strip foundation is being constructed with a reinforced belt made of metal bars and knitting wire. On top of the foundation structure, a frame and floor sheathing are installed for the future frame house. For the manufacture of the foundation, materials such as geotextiles, sand, gravel, edged boards for formwork, waterproofing, film, reinforcement, knitting wire will be needed. The total cost is 46,978.20 rubles. Waterproofing of the foundation on the upper part - 734 rubles. It is necessary to prepare material for the frame of the floor of the first floor - this is waterproofing, floor beams, rough and finishing floors, insulation. The total cost is 29488.20 rubles.
2. The design of the first floor for a frame house involves a separate assembly of each wall, including insulation, installation of windows and doors, exterior and interior cladding.
   • wall 1 (stands, strapping beams, braces, insulation, OSB outer cladding, drywall inner cladding, vapor barrier) - 40,717.20 rubles;
   • wall 2 (racks, strapping beams, braces, window 120 * 120, insulation, outer and inner lining, vapor barrier) - 18810.00 rubles;
   • wall 3 (stands, strapping beams, braces, window 120 * 120, insulation, outer, inner lining, vapor barrier) - 14,598.00 rubles;
   • wall 4 (pillars, beams, braces, window 57 * 50, insulation, sheathing, vapor barrier, metal door) - 16,996.00 rubles;
   • wall 5 internal (racks, beams, braces, insulation, sheathing) - 2,550.00 rubles;
   • wall 6 internal (pillars, beams, braces, insulation, sheathing, door leaf made of beech 900 * 2000) - 7,649.50 rubles;
   • wall 6 internal (pillars, beams, braces, insulation, lining, door leaf made of beech 700 * 2000) - 3,882.00 rubles;
   • the ceiling of the first floor (plasterboard lining) - 2,820.00 rubles.
3. Second floor for a frame house:
   • floor frame, materials for the floor itself (floor beams, cranial bars, subfloor, insulation, finishing floor, vapor barrier) - 22,434.00 rubles;
   • wall 1 (stands, beams, insulation, sheathing, vapor barrier) - 7,358.50 rubles;
   • wall 2 pediment (racks, beams, insulation, sheathing, window 90 * 120, vapor barrier) - 20,104.00 rubles;
   • wall 3 (stands, beams, insulation, sheathing, vapor barrier) - 7,358.50 rubles;
   • wall 4 pediment (racks, beams, insulation, sheathing, window 90 * 120, vapor barrier) - 16,492.00 rubles;
   • wall 5 (pillars, beams, insulation, sheathing) - 3,822.50 rubles;
   • wall 6 (pillars, beams, door leaf 900 * 2000 beech, insulation, lining) - 4,420.96 rubles;
   • ceiling of the second floor (frame made of edged boards, plasterboard lining) - 2,964.00 rubles.

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Roof, stairs and plumbing: we are building a solid building

Roof for a frame house on 2 floors with an ondulin roof (rafter system, lathing, insulation, inner lining, overhangs, ondulin, wind and hydro protection, vapor barrier) - 38,694.00 rubles. To make a two-story frame house with your own hands, you need to equip an interfloor staircase. For a simple wooden staircase of a direct type, it is necessary to prepare an edged board for the frame and steps, balusters, railings, bowstrings, self-tapping screws for fasteners. The total cost of materials is 3,982.00 rubles.

Any do-it-yourself frame house on the wall construction floor involves the wiring of engineering networks. For electricians, it is necessary to use materials such as 4.51 mm wires, anchor hangers for fasteners, a 32A machine, an electrical panel, a meter, an RCD, electrical cables for wiring to points, sockets, switches, ceiling lamps, energy-saving light bulbs. The total cost is 11,547.96 rubles.

Do-it-yourself frame house 6 * 6 should immediately include the wiring of plumbing systems. This includes a pump, clamps and hoses for connections, pipes for water supply and sewer pipes, faucets, doubles, thermal insulation for pipes, a washbasin, a toilet bowl, a sink, a bathtub, a shower cabin. The total cost is 24,337.40 rubles. In any construction, it is necessary to take into account consumables, which include nails, screws, bolts, metal corners and plates, sealant, anchors, putty, antiseptic, construction tape and much more. The total cost is 9,880.00 rubles.

To build a frame house 6 * 6 m from wood, an amount of approximately 350,000 rubles is needed, including the necessary engineering networks. Plus, additional costs will be required if you want to make a porch, balcony, veranda, as well as separate funds will be required for decoration. But again, we pay attention to the fact that the prices for building materials in each region are different.

A board for a frame house is the basis, the skeleton, which creates the basis of a modern frame house. That is why a random choice of a board will have the most negative consequences for the exterior and interior decoration of a frame house.

So, where are boards used in the construction of a frame house:

Boards bottom trim

Which rests on a concrete foundation, usually a 38 x 150 mm (2"" x 6"") impregnated board with an antiseptic. Fits in 1 layer. It is the impregnated board that is used, and not painted or submerged in an antiseptic bath. It is very important that the lower strapping board has clear geometric dimensions on four sides, since any deviations in dimension will immediately affect the horizontalness of the floor platform and the external geometry of the frame house. It is allowed to use two binding boards if you need to level the horizontal level before installing the floor log. Alternatively, you can use a larch board instead of impregnated pine or spruce. Larch wood resists decay well and can be used as a bottom trim board;

Floor log boards

Boards are used both for the entire floor joist structure and in combination with wooden I-beams, LVL-beams and floor trusses. For logs, boards with a section of 38 x 140-286 mm are usually used. The choice of section depends on the length of the overlapped span. The step and section of the boards can be viewed in the table in the section Floor joists. It is very important for the log that the moisture content does not exceed 19% at the time of construction, that is, it is not a cut board of natural humidity.

These must be chamber dried or dried for at least 4 months in a blown pile. Otherwise, wet boards will continue to dry after laying, which will lead to cracks and deformations. For floor logs, it is not allowed to use lumber with multiple defects: knots, cracks, wane, etc., as this weakens their structural capabilities. However, it is allowed to use light sabers, which are stacked with a bulge up. In the process of loading from above, this defect usually disappears. It is important that the boards for the floor lag of the frame house have a single size in width, as this directly affects the horizontalness of the platform. Otherwise, the floor may start to creak. For the floor log, it is necessary to use high-quality edged boards or cut them to one size on a thickness gauge or planer;

Boards for frame walls

Boards are used for frame racks, strapping, window and door openings. For walls of frame walls, boards with a section of 38 x 140-184 mm are used; for internal - 38 x 89-140 mm. The stud spacing for exterior walls is 407 mm or 610.5 mm (16"" and 24"" respectively) and corresponds to the dimension of plywood or osb / OSB outer sheathing sheets 1220 x 2440 mm (4""x8""). The dimensions of the boards in America are different from those stated. For example, a board with a section of 2""x6"" is actually not 50 x 152 mm, but 38 x 140 mm. From the sawmill, the boards come out of the declared size, but in the process of drying and gouging they lose weight. Actual board dimensions:

• 2""x2"" = 38 x 38 mm;
• 2""x4"" = 38 x 89 mm;
• 2""x6"" = 38 x 140 mm;
• 2""x8"" = 38 x 184 mm;
• 2""x10"" = 38 x 235 mm;
• 2""x12"" = 38 x 286 mm.

For frame racks, boards with a moisture content of not more than 19% are also used, that is, these boards must first be dried. It is very important that these boards are well sized or planed to a minimum width. Subsequently, sheets of outer and inner cladding are attached to them. It is possible to correct differences of 3-5 mm, but it is better to avoid this, since the process of leveling the frame racks itself takes time. As in the case of floor logs, sabers can be used, but they must be installed in one direction: for external walls, bending inwards, for internal walls, simply in one direction.

For frame racks, boards with minor defects can be used: resin pockets, knots, wane, etc., since their task is to withstand vertical loads. For short racks under windows, above doorways, you can use boards of short length, which remain after laying the logs and strappings. You can also cut good pieces from defective boards and use them in these knots. For double and triple frame racks, it is necessary to choose boards that are planed or even on all sides. This achieves a good fit of the racks to each other and reduces the risk of a gap in the future. For frame racks, it is convenient to saw 6 meter boards into two parts, which allows you to build frame houses with 3 meter ceilings. Although the ceiling height is usually 2.4 m (8") in Canada and the USA. Frame stud boards must be carefully trimmed and uniform in size. This allows the following floors of the frame house to be level;

Boards of the truss system of a frame house

The rafter system of a frame house usually consists of powerful ridge beams, the rafters themselves and various options for battens and counter battens. For ridge beams, boards that are even in length are used, dried to a minimum of 19%, from which a single ridge is assembled. The cross section of such boards depends on the angle of the roof and the length of the ridge beam and is usually in a wide range of 38 x 89-286 mm. There are several options for connecting boards into a single skate. The choice very often depends on the availability of lumber of the right size. For example, a ridge beam 11 meters long and 286 mm wide can be made from two boards with a section of 38 x 286 x 6,000 mm, washed down at a V-angle, or from four boards with a section of 38 x 140 x 5-6000 mm with a Z-shaped connection .

For rafters, boards with a section of 38 x 89-235 mm are used. The step and section of the boards depends on the length of the span covered by the rafters, the presence of struts, puffs. The choice of the optimal section of the board for the truss system can be found in the tables (section Roof of a frame house). If the standard 6 meter length boards are not enough, then the boards can be spliced ​​along the length using nails and bolts. For the rafter system, boards that have undergone a drying procedure (chamber or atmospheric) are also used. It is allowed to use boards with minor defects (knots, wane), if this does not affect the bearing capacity of the rafters. Light sabers are installed with a convexity upwards, the load of the roof should return them to a level state. Boards for rafters should be the same in width, so they should be selected very carefully. In case of a difference in the width of the rafters, it is necessary to first plan or program through the thickness gauge.

Board for crates. For some roofs, it is necessary to mount a batten and a counter batten, which together with the windproof membrane create a ventilated roof space. For battens and counter battens, boards and bars with a section of 25-50 x 50-100 mm are used. For these purposes, edged boards of natural moisture can be used, since, for example, an inch crate 25 x 100 mm attached to the rafters will dry with little or no deformation. With regard to the bar, the choice of material is strongly influenced by the quality of this lumber. Usually the bars are sold in packages of 6 pieces and 3 m long. Rogue merchants put bars with deformations, wane, damaged by fungus inside the package. Before buying, it is necessary to open each bundle and selectively check the section of the bar with a caliper and reject low-quality bars. Very often, bars with a section of 40 x 40, 40-50 and 50 x 50 mm can simultaneously fall into 1 package. Check - this is the guarantee that you will buy high-quality lumber;

Board for spacers, blocks for frame walls.

Between the lags, as well as the frame racks of the internal walls, fixing and fire blocks are installed. Usually, trimmings are used for this, which remain after trimming the frame racks, strapping boards and floor logs. There are no special requirements for blocks, as these are short pieces of normal lumber. Check the width before installation, as the platform sheathing rests on the blocks between the joists and the block boards must have the same width as the floor joists. With a competent calculation of the lumber of a frame house, the waste of boards will be no more than 10%. Moreover, many trimmings will then be used for embedded boards in the construction of frame walls, in order to subsequently attach plumbing fixtures, hanging furniture, and drywall to them. Therefore, do not store trimmings as construction debris in the open;

6) Jaws

For jibs that cut into the frame racks of external walls and strapping boards, you can use boards with a section of 25-38 x 100 x 200 mm. Usually, boards with pronounced defects (deformations, resin pockets, knots, etc.) go to the jibs - everything that was rejected during the construction of a frame house. Due to the fact that the jibs cut hard and are nailed to the posts, you can even level boards that are deformed in two planes.

A beam with a section of 100-200 x 100-200 mm is usually used for arranging verandas and terraces. The use of timber for corner posts threatens subsequently with freezing of the corners of the frame house; if you decide to use timber to strengthen the floor lag, then you must choose dried lumber, since raw timber is subject to significant deformation during drying. In our markets, it can be difficult to choose a beam of the required size if you decide to combine it in the ceiling with plank joists. It is more reliable to use double and triple boards reinforced with threaded studs or bolts. In this case, the price will be in favor of the boards.

8) Bars for crates

Bars with a section of 40-50 x 40-50 mm are used for the installation of internal or external crates. If you are planning a cross-frame installation, then after installing the slab insulation between the frame racks of the outer walls, flat (calibrated or planed) bars are nailed in a horizontal direction in increments of the size of the insulation. Thus, the "cold bridges" are blocked. Then a vapor barrier and a vertical crate of an inch board for drywall are installed. The device of the outer crate of even (calibrated or planed) bars involves the installation of horizontal siding in the future. There is no need to prepare that by saving and choosing bad quality bars, you will get a crooked facade or burst drywall.

Carefully approach the choice of boards for. The difference in price between the cheapest offer - edged board of natural humidity and planed boards of chamber drying can reach 60-100%. You can compensate for this difference with the speed of assembly of the frame, the lightness and quality of the finish. Be prepared for the fact that even if you buy high-quality lumber, some of the boards will turn out to be unsuitable at first glance. Subsequently, you will use them for girders, short posts, fixing leveled walls of a frame house, scaffolding and building platforms. On a general scale, the cost of the highest quality boards does not exceed 7-10%. If it is not possible to buy planed lumber, then try to agree on the choice of boards in order to pick up boards of the same dimension of good quality.

I specifically do not consider the use of glued laminated timber, LVL beams or as an alternative to boards, as they will be discussed in the following sections of the site.

Frame houses are built using modern advanced technologies. The structure of the house itself consists of two components: the frame and components, such as external and internal skin, heat-insulating fillers. The frame can be either wooden or metal. Such a house is very strong, durable. Subject to the construction technology, in such a house it will be warm and cozy.

Frame house project

Without a preliminary plan, the construction of a frame house is unrealistic. The frame house project includes the following design stages:

1. Designing the layout of the position of the frame house, in accordance with the rules and standards for the placement of a residential building on the site;
2. Architectural Engineering– creation of a house plan, drawings, calculation of the required amount of building materials;
3. Structural design includes the choice of the type of foundation, the shape of the frame of the house, floors, the shape of the roof;
4. Heating system design, ventilation, sewerage, water supply and electricity systems;
5. Cost calculation materials and work of builders, workers;
6. Organization of construction;
7. Arrangement of the site.

Features that distinguish frame houses

Frame houses have a number of advantages:

• Strength and durability the designs of such a house are determined by the features of the frame, the frequency of vertical beams and their thickness;
• low cost construction and operation;
• Simplicity and high speed of construction;
• Environmental friendliness;
• Can be built at any time of the year.

For the construction of frame houses, there are several recommendations that can facilitate the construction and operation of a frame house, help to avoid some mistakes during construction. When choosing materials and performing construction work the following tips should be followed:

• To build a frame house correctly, it is necessary to use wood with a moisture content of no more than 10-15%. Such wood is practically not deformed;
• It is better to take building materials with a small margin;
• The columnar foundation must be driven in 20-30 cm deeper than the freezing level;
• All wooden building materials must be treated with a special impregnation to protect against rodents and fire;
• All work must be carried out sequentially, according to plan;
• Before starting construction, it is necessary to work out the design of the house as carefully as possible, it will be very difficult and expensive to redo it later.

Foundation

Building a house begins with laying the foundation. For frame houses usually use two types of foundation: tape and columnar (piles). The choice depends on the following conditions:

• Ground water level;
• The level of soil freezing;
• Soil type;
• The mass of the structure of the house.

Before erecting the foundation, it is necessary to determine what elements and materials it will consist of. The dimensions of these elements, the method of reinforcement, the composition of the concrete solution. If a columnar foundation will be used, it is necessary to determine the distance between the columns and their number, as well as the depth of driving in these columns.

Floor frame

After the foundation has been erected, it is necessary to construct a floor frame, without which further construction of a frame house is impossible.

The floor frame is created as follows:

1. First you need to fix the bottom trim boards on the foundation. Elements are installed on the edge. The size of the boards, on average 15x5 cm;
2. Connect, with self-tapping screws or dowels, the boards of the lower internal trim in the corners;
3. Boards of the middle part of the lower trim are attached to the inner boards;
4. It is necessary to attach the outer boards to the middle boards;
5. Before proceeding to the next step, you need to make sure that the structure is even. Excess is removed with an electric planer;
6. It is necessary to mark the places where the lags will be installed. With the help of a jigsaw in the harness, grooves are made for inserting a log;
7. After installing the lag, wooden slats are attached between them. They will serve as supports;
8. a subfloor is laid on top of the slats. Usually, sheets of moisture-resistant OSB or plywood are used in this capacity;
9. From above, between the lags, a heater is laid: mineral wool or polystyrene. Lay the necessary communications: water supply and sewer pipes;
10. A vapor barrier film is laid over the insulation. The film is glued. Boards are laid on top, 3 cm thick at a distance of 40-60 cm from each other;
11. A tongue-and-groove board 2.5-3 cm thick is laid on top of the resulting lattice, screwed with self-tapping screws or nailed.

On the resulting flooring, you can lay any floor covering.

Ventilation

The ventilation of a frame house must be clearly defined and thought out at the design stage. With proper ventilation, the house will be provided with an optimal microclimate.

Ventilation can be:

• Natural(windows, windows, ventilation pipes);
• Artificial with an installed fan (for example, a kitchen hood);
• combined, when both types of ventilation are used;
• Combined with air heating system.

Ventilation is simply necessary in the kitchen and toilet. At the same time, thanks to the special design of the house, all ventilation elements can be hidden behind the walls.

Wall insulation

Thermal insulation begins with the selection of insulation. Usually used in this capacity: polystyrene, polystyrene, mineral wool.

Thermal insulation of walls is carried out according to the following stages of work:

• Surface preparation. The walls are cleaned of dust and dirt, protruding nails, etc.;
• All cracks must be sealed with mounting foam;
• Installing the crate and fixing the insulation on it;
• If polystyrene or polystyrene was used as a heater, then the gaps between the sheets must be filled with sealant;
• The frame of the house, along the perimeter, is upholstered with a special vapor barrier film. Instead of nails, staples and a construction stapler are used;
• Sheathed with sheets of drywall or OSB.

truss system

The truss system is the supporting structure of the roof. The stability of the house and the quality of the roof depend on how well it is made.

The construction of the truss system takes place in the following stages:

1. You must select the type of truss system. The rafter system consists of two rafter legs. can be built on the basis of two types of rafter system: inclined and hanging;
2. Choose the materials from which the frame will be assembled;
3. Install Mauerlat. Mauerlat - these are wooden bars that are laid around the perimeter on the load-bearing walls of the house, to evenly distribute the entire mass of the roof, in order to avoid distortions;
4. Install rafters. In the Mauerlat, grooves are made at a distance of no more than 1.5 meters from each other. Rafter legs are inserted into the grooves, the lower parts are fastened with a strapping. When installing rafters, it must be borne in mind that they should protrude 30-40 cm beyond the perimeter of the house. If the width is within 6 meters, then the hanging rafters are connected by a transverse beam;
5. They make a roof sheathing. The type of sheathing depends on what type of roofing material will be used.

Self-assembly errors

During the self-construction of a frame house, the following may be allowed, the most common mistakes:

• Purchase of raw wood;
• Violation of wall construction technology, some component was not installed or installed incorrectly (for example, insulation was not installed);
• Mistakes made during the construction of the frame, too rare or, conversely, too dense crate;
• Violations in the construction of door and window connectors, which must be reinforced with a special rack.

Appearance Options

Prove that the checkerboard is 10X10 cannot be cut along grid lines into rectangles 1X4. (Solutions according to D.Yu. Kuznetsov.)

Solution 1 . Divide the board into 2x2 squares and color them in a checkerboard pattern (Fig. 1). Note that any 1x4 rectangle contains equally (2) black and white cells, but with this coloring, there are 52 black cells and 48 white cells on the board, i.e. not equally. This means that it will not be possible to cut a 10x10 board into 1x4 rectangles.

Solution 2 . Let's color the board with a diagonal coloring in 4 colors (Fig. 2). Note that any rectangle contains one cell of each of the four colors, but with a given coloring, there are 25 cells of the 1st and 3rd colors on the board, 26 cells of the 2nd and 24 cells of the 4th, i.e. not equally. This means that it will not be possible to cut a 10x10 board into 1x4 rectangles.

1. Cut out the lower right and left corner cells from the chessboard. Is it possible to cut the resulting figure into 1x2 dominoes? And if you cut the bottom right and top left?

2. Is it possible to cut a 6x6 board into dominoes so that there are exactly 11 horizontal ones among them? (Horizontal coloring in two colors.)

3. Color the drawing in four colors so that adjacent parts are painted in different colors. Is it possible to get by with three colors? (See Activity 6: Coloring a Map - Grades 5-6).

4. In a 4x4 square, the cells of the left half are painted black, and the rest white. In one operation, it is allowed to recolor all the cells inside any rectangle in the opposite color. How to get a chess coloring from the original coloring in three operations?

5. Several grasshoppers sit on the same straight line, and the distances between neighbors are the same. Every minute one of them jumps to a point symmetrical to it with respect to another grasshopper. Can after some time the grasshopper Sasha end up in the place where his neighbor Lyosha was sitting at the beginning?

6. a) Is it possible to cut a chessboard into figures consisting of 4 cells in the shape of the letter "T"?

b) Is it possible to cut a 10x10 chessboard into such figures?

7. Is it possible to split an 8x8 square with a corner cut off into 1x3 rectangles?

8. Can a 10x10 board be cut into pieces of four cells in the shape of the letter "L"? (Horizontal coloring in two colors.)

9. An 8x8 board is cut into 2x1 dominoes. Can there be 15 vertical and 17 horizontal dominoes?

10. The triangle is divided into triangles (25 pieces), as shown in the figure. The beetle can walk in a triangle, moving between adjacent (on the side) triangles. What is the maximum number of triangles that the beetle can pass through if it has visited each triangle no more than once?

11. What is the largest number of rhombuses, each of which is made up of two equilateral triangles with side 1, that can be cut out of an equilateral triangle with side 5 (see the figure of the previous problem).

12. The triangular castle is divided into 100 identical triangular halls. There is a door in the middle of each wall. How many rooms can be visited by a person who does not want to visit anywhere more than once?