PUZZLES of LEONID MOCHALOV

Pyramid

      The submitted set consists of 10 figures. They are formed from three cubes in all possible ways, connected horizontally - by sides or ribs, vertically – by quarters of sides. Collect a pyramid using all ten elements of a set.
      If you cope with this task successfully, that will be not trouble for you to collect the other beautiful, symmetrical figure - a tower.
      If you exclude the block A (the bar 3x1x1), nine remained elements will serve as a building material for collecting of inclined and flaky cubes.

Chess cube

The puzzle consists of eight contrasting painted cubes - white and black. The unrolling cubes are given in the drawing. It is possible to stick the cubes of strong paper or to take wooden cubes and to paint (or to paste over with a paper) their sides.
It is necessary to collect a cube 2x2x2 with "chess" colouring of each side using eight cubes, as shown in the drawing. Thus the following condition must be observed: it is possible to put cubes to each other only with equally painted sides.

Barcube

Colour puzzle

Cube from bars

Unit of "flat" elements

Colour cube

Small puzzle

Triangle cube

Crystal

Chess piece on a field

On a game field consisting of 25 checks and two partitions, there are 20 chess pieces: 10 chess pieces of one colour and 10 chess pieces of the other colour. For one move it is possible to move any chess piece on any free check using free checks. How many movies least should be made to change the places of chess pieces of different colours

Tigers in a trap

      In a square box 5x5 there are 24 bars 1x1 (the place of one bar is free). On four bars the guards are drawn, on the other four bars the tigers are drawn, on sixteen bars pieces of a lattice are drawn.
      In an initial position the tigers are in a trap, the guards are outside of a trap (there is an empty place it the centre of a box). Moving bars to the center of a box, it is possible to let out tigers, and to hide guards in a trap. How can you do it? How many bar moves least is required for this?
      Do you think it is possible to give back one guard to tigers?

Triangular chesspieces

Hidden cube

      The elements of a puzzle are the cube 3x3x3 (A) and cubes of the same size. In there angular part parallelepipeds are cut out: 1x1x1 (B), 1x1x2 (C), 1x2x2 (D) and 2x2x2 (E).
      The task 1. From elements of a puzzle collect a cube so that the small cube (A) is hidden inside the large cube.
      The task 2. Collect the large cube with the beforehand chosen element inside.
      The task 3. Scatter cubes on a table, choose any element of a puzzle and fix it in space, and then hide it inside the collected cube. Use for collecting of a "shell" remained elements.

Stacking of a prism (1/2 & 1/4)

Cube 6x6x6

Zigzag

Squareword

Squareword puzzle is played on a square which is divided into cells with words written in them.Most of the cells are empty to begin with. The task is to fill the empty cells with the available letters, so that in each vertical and horizontal row, and on the two big diagonals of the square, the letters are different.

Express-labyrinth

		Beginning with the square in the upper left corner, try to find a path to the bottom right corner that passes through every whire square only once. You may move horizontally and vertically, but not diagonally, and passing through black squares is forbidden. Moving horizontally and vertically, but not diagonally, you must pass through each square once (except for the two exceptions below). Your path may not cross itself, and must form a complete loop, ending where you began. You connot enter squares marked with an X. You must enter squares with a diagonal line twice, but you may not cross the line. You may move through squares with a diagonal T-shape only once, and only through the “free” half.Again, you may not cross the lines. Let us try to solve the sample puzzle. First of all, taking the rules into accountt, mark the parts of the route that already have conditions. The grid now looks like this: So how do you the path through the rest of the squares?

Cut-it puzzles

Cut the remaining figure into parts and make another square from them, using as few pieces as possible.

Winding road

Beginning with the square in the upper left corner, try to find a path to the bottom right corner that passes through every whire square only once. You may move horizontally and vertically, but not diagonally, and passing through black squares is forbidden.

Plan

      Using all 28 dominoes, make the word “PLAN” as indicated, so that:
      The sums of the dots in all four letters afe equal.
      The tiles are positioned according the rules of dominoes (with adjacent domino halves matching).

Fractions

Take the whole set of dominoes without the 0:0 tile. Considering the other tiles as fractions, situare them as shown in the picture. The sum of each row must equal the number of tiles in the row.

Rebuses

The square made of stones

Nine numbered stones are positioned as shown:
What is the smallest number of stones that can be removed to leave a number that is the square of whole number? Which stones must be removed?

Cross number

Place a number in each square so each of the horizontal and vertical rows of squares contains a different square number.

Many dots

      Connect dots with the same numbers by drawing lines between them, observing the following conditions:
      The lines must follow the grid, though they may make any number of turns.
      The lines may not intersect, nor may they touch the outer edge of the grid.
      The lines must be of the same length.
      All lines must be as long as possible.

Surprising numbers

Rotated square

Place the numbers 1 through 9 in the boxes of the rotated square so that five square numbers can be read horizontally.

Blue strand

BLUE = X², STRAND = X³

Cube and Cuboctahedron

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Mill and Beehive		Trick by Yuri Melnikov