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About Surajit Basu
Expertise
I can answer questions which are mathematical, logical, or wordplay related. I am not good at highly creative problems, or riddles.

Experience
I regularly do puzzles, and help out friends, teenagers. I read books written by Martin Gardener. I love the puzzles and Easter eggs in Douglas Hofstadter's Godel, Escher, Bach: an enternal golden braid.

Publications
A few examples of my writing: http://surajitbasu.sulekha.com/blog/post/2006/04/the-journey-down-the-number-line.htm

Education/Credentials
B. Tech. ( Computer Science), IIT Kanpur, India MBA ( Post-Graduate Diploma in Business Management), (Finance, Systems), IIM Calcutta, India

 
   

You are here:  Experts > Games > Puzzles > Puzzle Solving > geo puzzle has me stumped

Puzzle Solving - geo puzzle has me stumped


Expert: Surajit Basu - 3/13/2008

Question
Each letter corresponds to one single digit, 0-9. Each digit corresponds to only one letter. Solve so that MATH + TEST = CACHE

Answer
MATH
TEST
-----
CACHE
-----

C must be 1; assume it is not 0.. and it cant be anything else.


MATH
TEST
-----
1A1HE
-----

H+T = E or E + 10...H,T <> 0
T+S (maybe+1) = H or H + 10
A+E (maybe+1) = 1 or 11 ( clearly, even if one of them the other can't be 1)...
so, A+E (maybe+1) = 11 ..i.e A + E = 10 or 11
M+T + 1 = 10 + A

A can be = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Not really
A can be = 2, 3, 4, 5, 6, 7, 8, 9

MATH
TEST
-----
1A1HE
-----

if A is 9, then E is 2.
M+T+1 = 10 + 9 i.e. M+T = 18, not possible.
A can be = 2, 3, 4, 5, 6, 7, 8

if A is 8, then E is 2 or 3.
M+T+1 = 10 + 8 i.e. M+T = 17, not possible.

if A is 7, try it out same way, not possible.

if A is 6, then E is 4 or 5.
M+T+1 = 10 + 6 i.e. M+T = 15, Possible with M=8, T=7

Thus, M+T+1 = 10 + A
or, M+T = 9 + A
has some solutions for A,M,T
A,M,T = (6,8,7); (5,8,6); (5,6,8); (4,5,8); (4,8,5); (4,6,7); (4,7,6); (3,4,8); (3,8,4); (3,5,7); (3,7,5); (2,3,8); (2,8,3); (2,4,7); (2,7,4); (2,5,6); (2,6,5).

For each combination, try out what E can be..A+E ends in 1 !
So, E can have at best 2 values

And for each combination, check what H can be ( H+T is E or 10+E);
then see what T+S=H or 10+H tells you.

A little bit of work.. but try it...

and if you get stuck, followup
at surajit@gmail.com

good luck  

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