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  Number & Math Play

Hungry Hamsters
 
Q Five hamsters ? Arnie, Betty, Carl, Debby, and Ernie ? are learning to go through a maze. Each time a hamster reaches the end of the maze, it gets a pellet of food.

So far, Arnie has gotten four more pellets than Betty; Betty has gotten seven fewer pellets than Carl; Carl has gotten five more pellets than Debby; and Debby has gotten three more pellets than Ernie. Betty and Debby have gotten ten pellets between them.

How many times has each hamster gone through the maze so far? (Each hamster has gone through more than once.)


 
A Arnie has gone through 8 times, Betty 4 times, Carl 11 times, Debby 6 times, Ernie 3 times. The key fact is that Betty and Debby have gotten ten pellets between them.

There are only ten possible combinations that will add up to ten pellets, and since we know that each hamster got more than one pellet, we can eliminate four of them: Betty 0/ Debby 10, Betty 1/Debby 9, Betty 9/Debby 1, and Betty 10/Debby 0. Try the remaining six combinations. Betty 4/Debby 6 is the only one that will work.

Source: Barnes and Noble,Mensa Presents Mind Games for Kids,p.13