20th May 2005 at 01:00
Puzzles to test mathematical skills, set by Anita Straker. Solutions below

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This clock face has been divided into two sectors.

This sum of the numbers is one sector is 30 and in the other sector is 48.

1 Divide the clock face into two sectors, so that the sum of the numbers in each sector is the same.

2 Divide the clock face into three sectors, so that the sums of the numbers in each sector form three consecutive numbers.


Jade chose a positive whole number.

She multiplied it by 2, added on 5, then multiplied by the original number.

The result was 403.

What was Jade's number?

SOLUTIONS Clock face puzzles (age 7-12) 1. 10, 11, 12, 1, 2, and 3 sum to 39; 4, 5, 6, 7, 8 and 9 also sum to 39. The sum of the numbers 1 to 12 is 78; if the numbers in the two sectors have equal totals, each must be 39.

2. 3, 4, 5, 6 and 7 sum to 25; 11, 12, 1 and 2 sum to 26; 8, 9 and 10 sum to 27. The middle consecutive number must be one third of 78, or 26, so the consecutive numbers are 25, 26 and 27.

Jade's number (age 9-12) 13. As the last operation was to multiply by the original number, that number must be a factor of 403. 403 = 13 x 31. Trying 13 and 31, we get (13 x 2 + 5) x 13 = 403, but (31 x 2 + 5) x 31=2077.

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