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This problem follows on from Less is More.
See the Teachers' Resources of Less Is More for guidance on how this problem could be used in the classroom.
Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. Try lots of examples. What happens? Can you explain it?
Follow the clues to find the mystery number.
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?