Ken's Puzzle of the Week
Magic Snowflake
Put the numbers 1-13 at the corners of the 6-pointed snowflake to make each
diamond have the same sum. Minimize the common sum.
To compare answers, rotate & reflect your solution to put the smallest number
the top, and the next smallest clockwise.
Extension (added 6Feb2009): Find solutions for all possible sums.
Source: Original.
Solutions were received from Kirk Bresniker, Dan Chirica, Mark Rickert,
Joseph DeVencentis, and Bernie R. Erickson. The minimum sum is 21.
There are three solutions. Here is Joe's summary:
5
10 8 7 9
2 1 4
12 6 3 13
11
5
11 7 8 9
2 1 3
12 6 4 13
10
7
13 3 10 8
4 1 2
11 5 6 12
9
To achieve this sum, you must have 1 in the center and one of these
sets on the inner points: 2 3 4 6 7 8, 2 3 4 5 7 9, 2 3 4 5 6 10.
For the first set, 5 can only be in a diamond with 7 and 8, 13 with 3 and 4,
and 12 with 2 and 6. So these pairs of inner numbers are adjacent, and only
the first two solutions shown above work for the remaining diamonds.
For the second set, 6 can only be on a diamond with 9 and 5, 12 with 5 and
3. But 8 can only go with either 7 and 5, or 9 and 3, and neither of these
pairs is possible with the other diamonds
For the third set, 7 must go with 10 and 3, 8 with 10 and 2, and 9 with 5
and 6. 11 can go with 4 and 5 or with 3 and 6, but if you put it with 3 and
6, there is no solution. The third solution above is the only way to
complete the snowflake.
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