There are 17 girls and 12 boys on the playground. How many children, at least, would have to join them, so that they could be divided into two groups of equal sizes both containing equal numbers of girls and boys?
National Math Olympiad in Slovenia
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Solution
If the children form 2 groups of equal sizes such that each group contains boys and girls, then there must be girls on the playground at that time. This is an even number that must also be equal to the number of boys on the playground. In order for the number of girls to be even and equal to the number of boys, at least one girl has to join them, as well as at least 6 boys. Therefore, at least 7 children have to join.
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