From a 1947 competitive examination for high school seniors conducted by Stanford’s math department:
My grandfather’s papers included an old invoice:
72 turkeys $-67.9-
The first and last digits are illegible. What are the missing digits, and what was the price of one turkey?
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If -679- is divisible by 72, then it’s also divisible by 8 and by 9.
If -679- is divisible by 8, then 79- is also divisible by 8 (we can ignore the two leftmost digits because any multiple of 1000 is divisible by 8). Of all the possibilities for 79-, only 792 is evenly divisible by 8, so the last digit must be 2.
If -6792 is divisible by 9, then the sum of its digits must be a multiple of 9. That means the first digit must be 3.
If the total invoice was for $367.92, then one turkey cost $5.11.
(Via George Polya and Jeremy Kilpatrick, The Stanford Mathematics Problem Book, 2013. Thanks, Sid.)
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