Enigma 1270: Christmas star
17 December 2014
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From New Scientist #2426, 20th December 2003 [link]
If you place a number in each of the twelve circles on this star you can then calculate the “line-total” of each of the six lines by adding up the four numbers along the line. Similarly you can calculate the “triangle-total” of each of the six small triangles by adding up the three numbers around the triangle.
Your task is to place the numbers 1 to 12 in the circles so that each of the line-totals is the same, and there is a triangle-total larger than the line-total, and a triangle-total less than half the line-total.
What number is diametrically opposite 1? And what number is diametrically opposite 2?