After the construction of the warehouse, a certain number of tiles remained. They can be used to lay out a rectangular

After the construction of the warehouse, a certain number of tiles remained. They can be used to lay out a rectangular area in the area next to the warehouse. If you lay 15 tiles in a row, then there will not be enough tiles for a square area. When laying 13 tiles in a row, one incomplete row remains, and when laying in 14 tiles, an incomplete row also remains, in which there are 11 plates (s, s) less than in an incomplete row when laying at 13. How many tiles are left after building a warehouse?

Since when laying out 13 and 14 tiles in a row of rectangles does not work, but incomplete rows remain, the number of tiles is divided by 13 and 14 with residues.
The remainder of dividing any number by 13 cannot be more than 12. By assumption, this number is 11 more than the remainder of dividing by 14. But the remainder of dividing by 14 is also not zero. This means that the remainder from division by 13 can only be 12. And the remainder from division by 14 is 1.
The total number of tiles is less than 100, otherwise they would be enough for a square area with a side of 10 tiles. Among the numbers less than 100, you need to find one that is divisible by 13 with a remainder of 12 and by 14 with a remainder of 1. Having checked all numbers within 100, divisible by 14 with a remainder of 1, we get the answer: 77 tiles.