Below are three groups of three numbers each. Combine the numbers in each group using the standard binary operations (addition, subtraction, multiplication, division, and exponentiation) so that each group yields the same number.

1. 3, 15, 18
2. 10, 13, 36
3. 24, 27, 39

For an example, see the first problem.

(In reply to Attempt at a computer solution by Charlie)

These are the matches that were found by the program that matched up the output from the program given:

result                  eqtn. assoc   


-12                           2  2 36 / (10 - 13)


-12                           3  2 24 / (27 - 29)


-39                           1  2  3 *  (5 - 18)


-39                           2  1 (10 - 13) - 36


-8.333333333333333D-02        2  1 (10 - 13) / 36


-8.333333333333333D-02        3  1 (27 - 29) / 24


-87                           1  2  3 - (18 *  5)


-87                           3  1 (24 - 27) * 29


 12                           2  2 36 / (13 - 10)


 12                           3  2 24 / (29 - 27)


 26                           1  2 18 +  (5 +  3)


 26                           3  1 (24 - 27) + 29


 33                           1  2 18 +  (5 *  3)


 33                           2  1 (10 - 13) + 36


 39                           1  2  3 * (18 -  5)


 39                           2  1 (13 - 10) + 36


 59                           1  2  5 + (18 *  3)


 59                           2  1 (10 + 13) + 36


 8.333333333333333D-02        2  1 (13 - 10) / 36


 8.333333333333333D-02        3  1 (29 - 27) / 24


 87                           1  1 (18 *  5) -  3


 87                           3  1 (27 - 24) * 29

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The eqtn. column identifies the set of numbers used, and the assoc column lists which operator was done first. I've put parentheses around those, even when not needed, for clarity.

Posted by Charlie on 2004-01-22 11:32:29