Find the fake! 2 children's problems about weighing coins

First, 7 coins must be laid out on each bowl. If one of the bowls is lower than the other, then a fake is in it. If the bowls remain in balance, then the fake will be found in a pile that did not lie on the scales.

After it became known where the fake lies, you need to do the following: divide this pile and put 3 coins on each bowl, and leave one on the table. If the bowls are in balance, then the remaining coin is counterfeit. In this case, only two weighings are required for verification.

If some bowl outweighs, then a fake is one of the three coins on it.

Then it remains to do the last, third weighing: take a bunch of three suspicious coins, put one on the scales, leave one on the table. If the scales are in the same position, then the fake is on the table, and if one of the bowls outweighs, then the desired coin is on it.

Answer: a counterfeit coin can be detected in three weighings.

This problem is solved in a similar way. Only now the coins need to be divided into three parts so that their number is approximately the same in each of the piles, in two of them the coins should be equal. It turns out 67, 67 and 66 coins.

If you put 67 coins on the scales and one of the bowls outweighs, then the heavier pile must be divided into 22, 22 and 23 coins. Then weigh the pieces of 22 coins.

If the scales are not balanced again, then the group must be divided into piles of 7, 7 and 8 coins. Now you have to weigh the piles of 7 coins again; if one outweighs, then it must be divided into piles of 3, 3 and 1 coins.

Conditions are obtained, as in the first problem, and then it remains to do two more weighings to find a fake. As a result, at least five weighings are required.

The same number of weighings will be required to check if the scales at the first step are in equilibrium. Then the fake will be in a pile of 66 coins, it must be divided into three equal parts of 22 coins. Then do another weighing and find a pile with a fake. It remains to be divided into piles of 7, 7 and 8 coins and then proceed in the same way as in the first case.

Answer: a counterfeit coin can be detected in five weighings.