Guest Posted August 10, 2009 Report Share Posted August 10, 2009 (edited) Substitute each of the capital letters in this 4x4 grid by a different digit from 0 to 9, such that the sum of each of the four columns as well as the sum of each of the four rows is TO. S H O P P I P E A R E A R E N T Note: TO represents the number 10*T + O. Edited August 10, 2009 by K Sengupta Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 10, 2009 Report Share Posted August 10, 2009 theres quite a few of them 8 i think (at least thats how many i found). The possible sums are 10 11 and 20 (and 0 if you count that) Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 10, 2009 Report Share Posted August 10, 2009 0=O 1=I T=2 R=3 A=4 P=5 N=6 H=7 S=8 E=9 8 + 7 + 0 + 5 = 20 5 + 1 + 5 + 9 = 20 4 + 3 + 9 + 4 = 20 3 + 9 + 6 + 2 = 20 20 20 20 20 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 10, 2009 Report Share Posted August 10, 2009 (edited) How can I edit a previous post? Edited August 10, 2009 by arnel Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 10, 2009 Report Share Posted August 10, 2009 How can I edit a previous post? you can only edit it if it's whithin ten minutes Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 11, 2009 Report Share Posted August 11, 2009 In order (0 - 9): O I T R A P N H S E with sum of 20. I liked this one. Finding one solution isn't too bad, but did anyone keep going and find 'em all? (I started by considering possible sums of 13,15,17,19,20,24,26,28). Unfortunately, by the time I finished, the next puzzle was posted :-) Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 11, 2009 Report Share Posted August 11, 2009 I think there is only one solution. A 4 E 9 H 7 I 1 N 6 O 0 P 5 R 3 S 8 T 2 Sum = 20 Someone mentioned possible sums of 0, 10, 11, and 20. Clearly zero is impossibel since the sum of any 4 positive integers is greater than zero. 11 is not a possible sum since that would mean T and O are both 1 which is not valid. 10 is also impossible since RENT and SHOP must equal the same sum and there are 8 different integers between them - no way to get a sum less than 14. If someone has a complete unique solution other than shown here, I would like to see it. Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted August 11, 2009 Report Share Posted August 11, 2009 Just for grins, I went through all 3,628,800 possible assignments of digits to letters. Only one solution popped out. I realize that I could have gone through a much smaller number given the constraints that could be surmised, put the program only took a few minutes to write and under a second to run. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 12, 2009 Report Share Posted August 12, 2009 Naah, there's only the one solution. I was just hoping I wasn't the only one who suffered trying to find another. :-) Quote Link to comment Share on other sites More sharing options...
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Substitute each of the capital letters in this 4x4 grid by a different digit from 0 to 9, such that the sum of each of the four columns as well as the sum of each of the four rows is TO.
Note: TO represents the number 10*T + O.
Edited by K SenguptaLink to comment
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