Can you arrange eight 8's so that when added they will equal 1000? Click below to see the answer.
It's certainly possible to try all 22 different ways to partition eight identical digits, but there is a shortcut.
All of the numbers that are created by arranging eight 8's will end in the digit 8, and the sum of the last digits of those numbers must be a multiple of 10 (because the target sum of 1000 ends in 0), so we know there must be exactly five groups of digits in the correct solution. That means we only have to check 3 different partitions of the eight digits.
8888 + 8 + 8 + 8 + 8
888 + 88 + 8 + 8 + 8
88 + 88 + 88 + 8 + 8
These are the only three ways to partition eight identical objects into five groups, and they are the only groupings whose sums end in the digit 0. You can check with quick mental arithmetic that the second grouping is the correct solution.
All of the numbers that are created by arranging eight 8's will end in the digit 8, and the sum of the last digits of those numbers must be a multiple of 10 (because the target sum of 1000 ends in 0), so we know there must be exactly five groups of digits in the correct solution. That means we only have to check 3 different partitions of the eight digits.
8888 + 8 + 8 + 8 + 8
888 + 88 + 8 + 8 + 8
88 + 88 + 88 + 8 + 8
These are the only three ways to partition eight identical objects into five groups, and they are the only groupings whose sums end in the digit 0. You can check with quick mental arithmetic that the second grouping is the correct solution.
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