Question

В игровом кубике грани пронумерованы числами от 1 до 6. Из пяти таких кубиков составили башню (поставили один на другой) и подсчитали сумму чисел на всех внешних гранях. После снятия верхнего кубика эта сумма уменьшилась на 19. Какое число могло бы быть на верхней грани нового верхнего кубика.​

Answer 1

Вроде бы должно быть 5

Answer 2

Problem Analysis

We are given that there are five dice, each numbered from 1 to 6, and they are stacked on top of each other to form a tower. The sum of the numbers on all the outer faces of the tower is reduced by 19 after removing the top die. We need to determine the number that could be on the top face of the new top die.

Solution

Let's assume the number on the top face of the new top die is x.

The sum of the numbers on all the outer faces of the original tower is 5 times the average of the numbers on the dice, which is (1+2+3+4+5+6)/6 = 3.5. Therefore, the sum of the numbers on the outer faces of the original tower is 5 * 3.5 = 17.5.

After removing the top die, the sum of the numbers on the outer faces of the tower is reduced by 19. Therefore, the sum of the numbers on the outer faces of the new tower is 17.5 - 19 = -1.5.

Since the numbers on the dice are integers from 1 to 6, it is not possible to have a negative sum. Therefore, there is no possible number that could be on the top face of the new top die.

Conclusion

There is no possible number that could be on the top face of the new top die.