[Guest]

Substitute each of the capital letters by a different digit from 0 to 9 to satisfy this system of cryptarithmetic equations. Each of T and N is nonzero.

W^D+I = TFLE and, D^H+N = NIWO

[Guest]

8³⁺¹=4096 and 3⁵⁺²=2187

I actually kinda came across this one on dumb luck, hard plugging numbers in to try to figure this out. Still working on a way to make it easier for myself to do these. They're interesting and I'm starting to enjoy them more and more. Now to go try your other one

[Guest]

If you list the powers of the positive integers that have exactly 4 digit answers, there are only 14 possibilities. Eliminate the three powers of 5 & 6 since they end in 5 or 6 and thus can't be answers. Eliminate the two results that have repeated digits since they can't be answers either. Elimnate the powers of 4 that have a 4 in them and the powers of 2 that have a 2 in them. You now have only 4 possible answers which are easy to test.

[Guest]

w D+1 TFLE TFLE D H+N NIWO NIWO NIWO NIWO w N

2 10 1024 9 4 6561 6 6

3 7,8 2178 6561 6,7 4,5 1296 7776 2401 9,7 1,2,7

4 5,6 1024 4096 4,5 5,6 1024 4096 3125 2,9 1,3,4

5 5 3125 4 5,6 1024 4096 2,9 1,4

6 4,5 1296 7776 3,4 5,6,7,8 2178 6561 1024 4096 7,6,2,9 1,2,4,6

7 4 2401 3 7,8 2178 6561 7,6 2,6

8 4 4096 3 2178 6561 7,6 2,6

9 4 6561 3 2178 6561 7,6 2,6

W 1,3,4,5,8 couldnt be

D 1,2,6,7,8 couldnt be

the first and second W must br same so the W can be 6 or 7.

so D=3 or 4

if W=6 so D=3

if W=7 so D=3

so D is equal 3!!!!!!!!!!!!

because of D=3 n just can 2 or 6:

w D+1 TFLE TFLE D H+N NIWO NIWO NIWO NIWO w N

6 4,5 1296 7776 3,4 5,6,7,8 2178 6561 1024 4096 7,6,2,9 1,2,4,6

7 4 2401 3 7,8 2178 6561 7,6 2,6

we can make the table smaller because d=3:

w D+1 TFLE TFLE D H+N NIWO NIWO NIWO NIWO w N H

6 4 1296 - 3 7,8 2178 6561 - - 6 2,6 5,6,1,2

7 4 4096 - 3 7,8 2178 6561 - - 7 2,6 5,6,1,2

we can make the table smaller because the numbers should't be repeatitive :

w D+1 TFLE TFLE D H+N NIWO NIWO NIWO NIWO w N H

6 4 1296 - 3 7,8 2178 6561 - - 6 2 5

7 4 4096 - 3 7,8 2178 6561 - - 7 2,6 5,6,1,2

NIWO has not to have repeatitive number:

w D+1 TFLE TFLE D H+N NIWO NIWO NIWO NIWO w N H

6 4 1296 - 3 7 2178 - - - 6 2 5

7 4 4096 - 3 7 2178 - - - 7 2 5,6

w must be 7!!!!!!!!!

7^4=4096 3^7=2178

w=7 d=3 t=4 f=0 l=9 e=6 n=2 i=1 o=8 h=5!!!!!!!!!!!!!

Edited August 12, 2009 by nima