Guest Posted August 1, 2009 Report Share Posted August 1, 2009 (edited) In this alphametic, each capital letter represents a different base ten digit from 0 to 9, where each of W and T is nonzero. WE + TO + WEE + WORD = THINK Determine the value of D such that the above equation has precisely one solution. Edited August 1, 2009 by K Sengupta Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 1, 2009 Report Share Posted August 1, 2009 In this alphametic, each capital letter represents a different base ten digit from 0 to 9, where each of W and T is nonzero. WE + TO + WEE + WORD = THINK Determine the value of D such that the above equation has precisely one solution. Hi there. This is my first time visiting this site and I enjoyed solving this puzzle. A bit of a brain-warp for the first few minutes, but definitely enjoyable. Thanks! I post my solution here for verification. Please do not read if you wish to solve for yourself! D=8 (H=0,T=1,O=2,I=3,K=4,N=5,R=6,E=7,D=8,W=9) Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 2, 2009 Report Share Posted August 2, 2009 D=8 W has to be 9 because is the only way you can achieve a 5 digit result T has to be one because no matter what numbers you put on the left, you can only get a 10 thousand number so H = 0 also So far we have: 9E + 1O + 9EE + 9ORD = 10INK Then logic told me that 2nd digit of WORD should not be big (because of the 9 hundred number) so I tried 2 and E=8 but could not find the answer so I figure E=7 97 + 12 + 977 + 92RD = 10INK Then the easy part. There is only 3,4,5,6 and 8 left. Found a combination that as a result gave me the number 10354 using 68 So: 97 + 12 + 977 + 926"8" = 10354 Don't know if it's the only solution but it is one at least On the other hand I was mixing logic with trial and error (not the best way to solve one of this I guess but it worked for me Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 5, 2009 Report Share Posted August 5, 2009 There is another solution using the value for D given above but there is a unique solution for a different value of D This was a brute force solution - I followed similar logic as above to narrow down the possible combinations to 7!/2 or 2520 and then wrote a short program to test all of the possible combinations. Don't know if there is a more elegant solution. W = 9 9 9 T = 1 1 1 H = 0 0 0 O = 2 4 3 I = 3 5 4 D = 8 8 2 E = 7 7 6 R = 6 3 8 N = 5 2 5 K = 4 6 7 D=2 has a single solution Quote Link to comment Share on other sites More sharing options...
Question
Guest
In this alphametic, each capital letter represents a different base ten digit from 0 to 9, where each of W and T is nonzero.
WE + TO + WEE + WORD = THINK
Determine the value of D such that the above equation has precisely one solution.
Edited by K SenguptaLink to comment
Share on other sites
3 answers to this question
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.