224. Boxes with Shells. Shells for six-inch howitzers were packed in boxes of 15, 18, and 20.

- Why do you have different boxes? - I asked the officer at the warehouse.
- You see, - he replied, - this allows us to deliver the required number of shells to the battery without opening the boxes.

Indeed, this system worked flawlessly when a large number of shells was needed, but it proved to be useless if, for example, 5, 10, 25, or 61 shells were required.

What is the largest number of shells that cannot be delivered to the battery in whole boxes, containing 15, 18, and 20 shells each? It is not too large.
224. An officer at the warehouse must issue the required number of shells in boxes of 18 shells until the remaining number of shells is a multiple of 5. If the number of shells is not 5, 10, or 25, the remaining shells should be issued in boxes of 15 and 20 shells. The largest number of shells for which the system fails is 72 plus 25, that is, 97. If the number of shells in the warehouse is greater, for example, 133, and 108 shells are packed in 6 boxes of 18 shells each, then the officer should issue only 1 box of 18 shells, and the remaining 115 shells should be repackaged into 1 box holding 15 shells and 5 boxes containing 20 shells each. If there are 97 shells in the warehouse, the officer will only have a remainder that is a multiple of 5, that is, 25 shells, after issuing 72 shells.