Monday

January 16, 2017
Posted by **Ian** on Friday, March 29, 2013 at 12:45am.

Details and assumptions

abc¯¯¯¯¯ means 100a+10b+1c, as opposed to a×b×c. As an explicit example, for a=2,b=3,c=4, abc¯¯¯¯¯=234 and not 2×3×4=24.

- Maths -
**Wayne**, Friday, March 29, 2013 at 10:20amab = 75

Archaic solution: only possibilities for ab are 01 through 99. Eliminate all of those not divisible by 5, which leaves: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55. 60, 65, 70, 75, 80, 85, 90, and 95. Eliminate those not divisible by 3 (divisibility rule for 3) , which leaves 15, 30, 45, 60, 75, and 90. Now eliminate those not divisible by 7, which leaves ab = 75. Divisibility rule for 7: double the last digit and subtract from the remaining digits. If the ramaining digits are divisible by 7, then the original number is divisible by 7. So, our number is 12075. 5 + 5 =10. Subtracting: 1207 - 10 = 1197. 1197mod7 has no remainder, thus our solution.