Question

Шоколадка имеет размер 4×104×10 плиток. За один ход разрешается разломать один из уже имеющихся кусочков на два вдоль прямолинейного разлома. За какое наименьшее число ходов можно разбить всю шоколадку на кусочки размером в одну плитку?

Answer 1

А как первый?
4/2 
2/2 2/2 
10/2 10/2 10/2 10/2
-------------------------------
10/2
4/2 4/2
2/2 2/2 2/2 2/2

Answer 2

Minimum number of moves to break the entire chocolate bar into pieces the size of one tile

To determine the minimum number of moves required to break the entire chocolate bar into pieces the size of one tile, we need to consider the dimensions of the chocolate bar and the allowed moves.

The chocolate bar has a size of 4x10 tiles. Each move allows us to break one of the existing pieces into two along a straight line. We want to break the entire chocolate bar into pieces the size of one tile.

To solve this problem, we can start by breaking the chocolate bar into smaller pieces until we reach the desired size. Since the chocolate bar has a size of 4x10 tiles, we can break it into two pieces of size 2x10 or 4x5. We can continue breaking these pieces until we have individual tiles.

Let's break down the steps:

1. Break the chocolate bar into two pieces of size 2x10. 2. Break each of these pieces into two pieces of size 2x5. 3. Break each of the 2x5 pieces into two pieces of size 2x2.5. 4. Break each of the 2x2.5 pieces into two pieces of size 2x1.25. 5. Finally, break each of the 2x1.25 pieces into two individual tiles of size 1x1.

By following these steps, we can break the entire chocolate bar into individual tiles of size 1x1.

The minimum number of moves required to break the entire chocolate bar into pieces the size of one tile is 9 moves.

Please note that the specific arrangement of the breaks may vary, but the number of moves will remain the same.