Advent calendar 2025
3 December
Holly picks the number 513, reverses it to get 315, then adds the two together to make 828.
Ivy picks a three-digit number, reverses it, then adds the two together to make 968. What is the smallest number that Ivy could have started with?
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If Ivy's number is ABC, then A+C must be 8 or 18 (as this makes this final digit of the sum correct). A+C cannot be 18 of the sum would be bigger than 1000, so A+C must be 8.
The middle digit tells us that 2×B must be 6 or 16. As the first digit of the sum is 9 and not 8, there must be a 1 carried over into the hundreds column, so 2×B = 16 and B = 8.
Overall, we know that Ivy's number is A8C, with A+C = 8. The smallest possible number Ivy could have started with is therefore 187.
