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 ten*ten – ten = ninety (Posted on 2009-10-25)
In this alphametic equation, each of the small letters in bold denotes a different base b digit from 0 to b-1. Neither t nor n can be zero.

(ten)*(ten) - ten = ninety

Determine the minimum value of b, for which there exists at least one solution to the above equation.

 No Solution Yet Submitted by K Sengupta Rating: 4.0000 (1 votes)

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 the code I used | Comment 2 of 5 |

DEFDBL A-Z
DIM used(100)
FOR b = 5 TO 100
FOR t = 1 TO b - 1
IF used(t) = 0 THEN
used(t) = 1
FOR n = 1 TO b - 1
IF used(n) = 0 THEN
used(n) = 1
FOR e = 0 TO b - 1
IF used(e) = 0 THEN
used(e) = 1
FOR i = 0 TO b - 1
IF used(i) = 0 THEN
used(i) = 1
FOR y = 0 TO b - 1
IF used(y) = 0 THEN
used(y) = 1

ten = t * b * b + e * b + n
ninety = y + b * (t + b * (e + b * (n + b * (i + b * (n)))))
IF ten * ten - ten = ninety THEN
PRINT b, t; e; n, n; i; n; e; t; y, ten; ninety
END IF

used(y) = 0
END IF
NEXT
used(i) = 0
END IF
NEXT
used(e) = 0
END IF
NEXT
used(n) = 0
END IF
NEXT
used(t) = 0
END IF
NEXT
NEXT

to get

`11            6  7  4       4  0  4  7  6  1            807  650442`

for the base, the numbers ten and ninety, and those values in decimal.

 Posted by Charlie on 2009-10-25 13:44:22

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