Elementary POW, January 13-17, 1997

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Which Hand Game
Give a friend an "even" coin (for example, a dime is even since 10 is an even number) and an odd coin (for example, a nickel, since 5 is an odd number). Ask him to hold one coin in his right hand and the other in his left.
Tell him to triple the value of the coin in his right hand and double the value of the coin in his left, then add the two.
If the sum is even, the dime is in his right hand. It the sum is odd, it is in his left hand.

Explain why this will always be true.

Try to think up a variation of this game.

This week's mentor is Jason Wickersham, a first-year college student at Las Positas college in Livermore CA. Jason is a physics/mathematics major currently studying multivariable calculus.

Highlighted Solutions

Sonja R.
Grade 4
Mrs. Sturtevant
Bagnall School, Groveland, MA
If the even coin is in the right hand, 3 times an even number is an even product. Two times the odd coin in the left hand is an even number too. If you add any of the products in the right hand to any of the products in the left hand you get an even sum. So an even sum means the even coin is in the right hand. If the odd coin is in the right hand, 3 times an odd number is an odd product. Two times the even coin in the left hand is an even number. If you add any of the products in the right hand to any of the products in the left hand you get an odd sum. So an odd sum means the even coin is in the left hand.

Julia Tomasko
Grade 4
Mr. Paul Nass
Georgetown Day School, Washington DC
The way that I figured it out was I tried it out on somebody and then I just figured it out. This is the answer that I got: Whenever you either double or triple the even coin, then you get an even number. When you double the odd coin you get an even number, but when you triple it you get an odd number. If the odd coin is in the right hand and you triple it, then you get an odd number and you add it to the even number and get an odd number. If that happens, then you will know where the coins are. If the odd coin is in the doubled hand, then you get an even number and add it to the other even number and get an even number. Then you also know where the coins are. My variation is to do everything the same except multiply the number in the right hand by four and do nothing to the number in the left hand.

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