14th October 2005 at 01:00
Circle sums

Use all the numbers 1 to 8.

Put one number in each empty circle.

The sum of any two adjacent numbers must be equal to the sum of the pair of numbers diagonally opposite.

Missing digits

Each * stands for a missing digit.

What is the answer to this multiplication problem?

SOLUTIONS Circle sums (ages 7 to 11): Working clockwise, the numbers are 10, 1, 4, 5, 8, 9, 2, 3, 6, 7.

Missing digits (ages 10 to 14): There are two possible answers: 345 x 37 = 12,765; or 345 x 68 = 22,760. The digit below the zero, and the digit to the right of the 6, must be 5 or zero. The digit to the left of the zero must be either 5 or 0, since there is no "carry" figure from the units column. The digit above the 6 must correspondingly be 1 or 6. You can work on from there to find the two possibilities.

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