Advent calendar 2025
12 December
Mary uses the digits 1, 2, 3, 4, 5, 6 and 7 to make two three-digit numbers and a one-digit number (using each digit exactly once). The sum of her three numbers is 1000.
What is the smallest that the larger of her two three-digit numbers could be?
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The sum of the units digits of the three numbers must be 10 (as the units digit of the result must be 0 and the number are not big enough to allow the sum to be 20). Similarly, the sum of the
two tens digits must be 9, and the sum of the two hundreds digits is 9 (so that 10s are made when the 1 is carried).
The> hundreds digits could be 2 and 7, 3 and 6, or 4 and 5. As we're looking to make the larger number as small as possible, we should pick 4 and 5.
The tens digits could be 2 and 7 or 3 and 6. We pick 2 and 7 and as 2 is the smallest possible number here.
Finally, the units digits are 1, 3 and 6. We use 1 for our number as it's smallest, leading to 521.
