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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Comments
Very cute story, and a wonderful teaser!
ooooooo....I was so close. I got stuck on D/E=F. I had it could only be either 8/2 or 6/2...I completely missed 6/3...it's always the really simple mistake that get ya! hee hee.....lotsa of fun getting stumped.
Nice problem. Very creative i like your style. Not impossibly hard and not too easy....
Fine problem. Got it after some trial and error. Fun trying out the various possibilities.
Fine problem. Got it after some trial and error. Fun trying out the various possibilities.
That was cool! I liked it a lot, it was moderate though...but Good one!
my kind of math teaser
Very nice teaser even though it only took a few seconds to solve.
Since F is involved in two products that produce a single digit it must be 2. That means that C and E are 3 and 4. Intuitively it seems that I must be larger than 6 to have enough smaller numbers left for G and H, so I becomes 8, C becomes 4, E becomes 3 and D becomes 6. That was the first couple of seconds.
The 9 has to go in A which forces the rest of the assignments. Under 10 seconds.
Since F is involved in two products that produce a single digit it must be 2. That means that C and E are 3 and 4. Intuitively it seems that I must be larger than 6 to have enough smaller numbers left for G and H, so I becomes 8, C becomes 4, E becomes 3 and D becomes 6. That was the first couple of seconds.
The 9 has to go in A which forces the rest of the assignments. Under 10 seconds.
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