Hello, ilikepizza!

There are four quality inspectors inspecting boxes.

A batch of boxes is numbered in order from 1 to 2500. each inspector is inspecting one part.

. . Every 5th box has its sticker inspected.

. . Every 7th box has its cardboard inspected.

. . Every 17th box has its logo inspected.

. . Every 23rd box has its packaging inspected.

1) Explain why no box is checked by all four inspectors.

The box which is first inspected four times is numbered with the LCM of the four numbers.

. .

Hence, box #10,465 would be inspected four times.

. . But there are only 2,500 boxes.

2) Make a list of the numbers of all the boxes which are checked by 3 inspectors.

Every 455th box would be inspected for its sticker, cardboard and logo.

These would be: #455, 910, 1365, 1820. 2275

Every 805th box would be inspected for its sticker, cardboard and packaging.

These would be: #805, 1610, 2415

Every 1495th box would be inspected for its sticker, logo and packaging.

This would be: #1495

Every 2093rd box would be inspected for its cardboard, logo and packaging.

This would be: #2093