### Brain Teasers

# Four Equations

Checkers, the smartest dog in the world, was doodling in his math diary and come up with three equations:

A-B=C

D/E=F

G+H=I

He was about to write a fourth equation using multiplication when an interesting thought occurred to him. Instead of using a new set of numbers (J, K, L) for his fourth equation, he would use the answers of the three existing equations:

C*F=I

Now the only question in his mind was, "Can I replace the letters A through I with the digits 1 through 9 in such a way that all four of my equations are correct?"

A-B=C

D/E=F

G+H=I

He was about to write a fourth equation using multiplication when an interesting thought occurred to him. Instead of using a new set of numbers (J, K, L) for his fourth equation, he would use the answers of the three existing equations:

C*F=I

Now the only question in his mind was, "Can I replace the letters A through I with the digits 1 through 9 in such a way that all four of my equations are correct?"

### Answer

Without too much thought or fanfare, and realizing that slight variations could occur, Checkers wrote the four equations using the digits 1 through 9:9-5=4

6/3=2

1+7=8

4*2=8

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