Cut the clock face into three parts with equal sums

Question

A clock face shows the numbers 1 to 12 in the usual circle. Draw two straight lines across the face so that it is divided into three regions, and the numbers inside each region add up to the same total.

What is the total, and where do the lines go?

Accepted Answer

Each region sums to 26. The two lines are parallel chords that do not cross. The target. The numbers 1 to 12 add to 78, so three equal regions hold 78 / 3 = 26 each. The lines. Two lines that cross inside the face would make four regions, so the lines must not cross: use two chords running roughly left to right. - The upper chord enters between 10 and 11 on the left and leaves between 2 and 3 on the right. Above it sit 11, 12, 1, 2, which add to 26. - The lower chord enters between 8 and 9 on the left and leaves between 4 and 5 on the right. Below it sit 5, 6, 7, 8, which add to 26. - The mid…

Cut the clock face into three parts with equal sums

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