Math Brain Teasers: The Puzzles

Any time I come across a math-y brain teaser, I just have to try to solve it. That's what happened when I read through the latest issue of Reader's Digest (August 2013) called "Fun and Games." I thought it would be fun to share these little teasers with you. Tomorrow, I will reveal the answers along with my process of finding the solutions, so make sure you subscribe to e-mail updates or check back then! These puzzles are the property of Reader's Digest.

Coin Counting

Jones gives Smith as many coins as Smith has. Smith then gives Jones as many coins as Jones has remaining. Now Jones has 36 coins, and Smith has 42 coins. How many coins did each of them have to begin with?

A Corny Question

A merchant has 21 sacks of grain: seven full, seven half-full, and seven empty. He wants to divide them equally among his three sons. How can he do this--without transferring any portion of grain from sack  to sack--so that each son will have not only an equal quantity of grain, but also an equal number of sacks?