Problem 3: A Three Digit Number
I am thinking of a three digit number. If you subtract 7 from it, the result is divisible by 7; if 8, divisible by 8; and if 9, divisible by 9. What is the number? Explain how you arrived at your answer.
Please submit all problem solutions to mathpotw@acu.edu before 5:00 PM on the next Thursday, October 7th.
Correct solutions were submitted by Wyatt Witemeyer.
Solution
No fancy software required, just a bit of brainpower and you see that the number in question
must be divisible by 7, 8, and 9. The LCM of these three is 504, and since no multiple of
504 is less than 1000, then this is our answer.
