A grocery clerk must stack thirty cases of canned vegetables. Each case contains twenty-four cans. He wants to display them in a pyramid, with each row containing one less can then the one below it. Is it posssible to use up all the cans and have a top row with only one can...How many rows of cans would he have?

Gnomon

No it is not possible to use all the cans exactly. It the base is a row of cans one can wide and the whole things is a flat pyramid, then the best he can do is start with 37 cans along the base and 37 rows, with 1 can in the top row. This will use up 703 cans of the 720, leaving him with 17 cans left over. If he makes a square base of 12 x 12 cans, puts another layer of 11x11 on top and continues to a top layer of 1 can, he will use 650 cans and have 70 left over. Nov 04 02, 3:17 PM

But...what if

he uses thirteen cans on the bottom row to one on the top, and he would have four cans deep as well. Nov 04 02, 4:58 PM