A new December and a new bunch of puzzles from mscroggs.co.uk.

Holly picks the 3-digit number abc. Then she removes either a, b or c to get a new 2-digit number. Adding these 2 numbers together gets 309. 309 is odd, therefore removing a digit from abc can’t preserve c as the last digit, as that would make the sum even. So we have:

309 = abc + ab

• c + b = 9 (can’t be 19)
• b + a = 10 or 0
• a = 3 or a + 1 = 3

If b + a = 0, a = 3 is impossible.

• c + b = 9
• b + a = 10
• a + 1 = 3

Therefore a = 2, b = 8, c = 1. So abc = 281.