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'A Mixed-up Clock' printed from http://nrich.maths.org/
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from the ten statements below?
Here is a clock-face with letters to mark the position of the numbers so that the statements are easier to read and to follow.
- No even number is between two odd numbers.
- No consecutive numbers are next to each other.
- The numbers on the vertical axis (a) and (g) add to $13$.
- The numbers on the horizontal axis (d) and (j) also add to $13$.
- The first set of $6$ numbers [(a) - (f)] add to the same total as the second set of $6$ numbers [(g) - (l)] .
- The number at position (f) is in the correct position on the clock-face.
- The number at position (d) is double the number at position (h).
- There is a difference of $6$ between the number at position (g) and the number preceding it (f).
- The number at position (l) is twice the top number (a), one third of the number at position (d) and half of the number at position (e).
- The number at position (d) is $4$ times one of the numbers adjacent (next) to it.