The 5 x 5 white area below is to be filled in with nickels, dimes and quarters, some of which have already been placed. Not every square need be filled; in fact one square marked with an asterisk (*) is definitely to be left without a coin. Only one coin is allowed per square. Some of the denominations have already been filled in to get you started.
The total value of the coins in each row is shown in the yellow square at the end of the row. The total value of the coins in each column is shown in the yellow square at the bottom of the column. The total value of each diagonal is indicated by the 60 and the 90 in the yellow squares of the very top row.
Fill in the remaining coins necessary to make the totals come out right.
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60
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90
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↘
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↙
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5
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60
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10
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10
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40
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25
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55
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75
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10
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*
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5
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30
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35
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55
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65
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30
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75
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From Mensa Puzzle Calendar 2022 by Fraser Simpson, Workman Publishing, New York. Puzzle for January 18.
in terms of 5 cents:
2 2 1 2 5
1 2 2 1 2
1 0 5 0 5
1 5 5 2 2
2 2 0 1 1
or in coins:
D D N D Q
N D D N D
N 0 Q 0 Q
N Q Q D D
D D 0 N N
I tried p&p first, but an efficient strategy proved illusive.
Rather than think too hard, I wrote a brute force code....
soln
