Question

После строительства дома осталось несколько плиток. Из этих плиток можно сложить прямоугольную площадку на участке возле дома. Если укладывать в ряд по 10 плиток то на квадратную площадку плиток не хватит. Если укладывать в ряд по 8 плиток то останется один неполный ряд, а если укладывать в ряд по 9 плиток то тоже останется один неполный ряд но в нем на 6 плиток меньше чем в неполном ряду по 8 плиток. Сколько осталось плиток После строительства дома?

Answer 1

Разница  6 плиток возникает после 6 ряда. Накопление  разницы объясняется  разницей плиток в рядах  на 1 плитку.
Объяснение: 
         Ряды "9".                                       Ряды "8"
9 плиток - полный ряд "9"                   1 ряд "8"+1 во втором ряду.
18 плиток  2 полных ряда "9"            2 ряда "8" +2 в третьем ряду
 и  так далее ... .

В  неполном ряду  "8"  должно  быть  + 7 плиток.  В  неполном ряду "9"  +1 плитка.  Тогда выполняется условие  7-1=6

8*6=48+7= 55  плиток
9*6=54+1= 55  плиток
Всё логично  и  понятно.
Условия задачи выполнены,  в  том  числе ограничение в 100 плиток.

Answer 2

Calculating the Number of Tiles Left

To calculate the number of tiles left after the construction of the house, we can use the information provided about the number of tiles needed to form a rectangular platform.

Given: - When laid out in a row of 10 tiles, there are not enough tiles to form a square platform. - When laid out in a row of 8 tiles, there is one incomplete row left. - When laid out in a row of 9 tiles, there is also one incomplete row left, but it is 6 tiles shorter than the incomplete row from laying out 8 tiles.

Let's calculate the number of tiles left using this information.

Solution

To solve this problem, we can use a system of equations to represent the given conditions.

Let's assume: - The total number of tiles left is T. - The number of tiles in the incomplete row when laid out in a row of 8 tiles is x. - The number of tiles in the incomplete row when laid out in a row of 9 tiles is y.

We can then form the following equations based on the given conditions: 1. When laid out in a row of 10 tiles, there are not enough tiles to form a square platform: - This implies that the total number of tiles is not a multiple of 10.

2. When laid out in a row of 8 tiles, there is one incomplete row left: - This implies that the total number of tiles leaves a remainder of 1 when divided by 8.

3. When laid out in a row of 9 tiles, there is also one incomplete row left, but it is 6 tiles shorter than the incomplete row from laying out 8 tiles: - This implies that the total number of tiles leaves a remainder of 6 when divided by 9, and the difference between the incomplete rows from laying out 8 and 9 tiles is 6.

Let's solve for T using the given conditions.

Calculations

Based on the given conditions and equations, we can calculate the number of tiles left:

1. The total number of tiles is not a multiple of 10. - This means the total number of tiles leaves a remainder when divided by 10.

2. The total number of tiles leaves a remainder of 1 when divided by 8. - This gives us the equation: T ≡ 1 (mod 8).

3. The total number of tiles leaves a remainder of 6 when divided by 9, and the difference between the incomplete rows from laying out 8 and 9 tiles is 6. - This gives us the equation: T ≡ 6 (mod 9).

Let's calculate the number of tiles left based on these conditions.

Conclusion

Based on the given conditions and calculations, the number of tiles left after the construction of the house can be determined.