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 Substitute seen, get result (Posted on 2007-05-10)
Substitute the letters S, E and N by valid digits to satisfy the following alphametic equation.

(SEEN)Base 8 - (SEEN)Base 5 = (SEEN)Base 7

NOTE: S is NOT zero.

 See The Solution Submitted by K Sengupta Rating: 3.0000 (1 votes)

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 method of exhaustion | Comment 3 of 4 |

There are only 48 substitutions to check out, given that no digit can exceed 4, as each must be acceptable within a base-5 number:

`subst decimal of   diff   decimal of       b8    b5             b71002   514 - 127 =  387     3451003   515 - 128 =  387     3461004   516 - 129 =  387     3471220   656 - 185 =  471     4551223   659 - 188 =  471     4581224   660 - 189 =  471     4591330   728 - 215 =  513     5111332   730 - 217 =  513     513 <--1334   732 - 219 =  513     5151440   800 - 245 =  555     5671442   802 - 247 =  555     5691443   803 - 248 =  555     5702001  1025 - 251 =  774     6872003  1027 - 253 =  774     6892004  1028 - 254 =  774     6902110  1096 - 280 =  816     7422113  1099 - 283 =  816     7452114  1100 - 284 =  816     7462330  1240 - 340 =  900     8542331  1241 - 341 =  900     8552334  1244 - 344 =  900     8582440  1312 - 370 =  942     9102441  1313 - 371 =  942     9112443  1315 - 373 =  942     9133001  1537 - 376 = 1161    10303002  1538 - 377 = 1161    10313004  1540 - 379 = 1161    10333110  1608 - 405 = 1203    10853112  1610 - 407 = 1203    10873114  1612 - 409 = 1203    10893220  1680 - 435 = 1245    11413221  1681 - 436 = 1245    11423224  1684 - 439 = 1245    11453440  1824 - 495 = 1329    12533441  1825 - 496 = 1329    12543442  1826 - 497 = 1329    12554001  2049 - 501 = 1548    13734002  2050 - 502 = 1548    13744003  2051 - 503 = 1548    13754110  2120 - 530 = 1590    14284112  2122 - 532 = 1590    14304113  2123 - 533 = 1590    14314220  2192 - 560 = 1632    14844221  2193 - 561 = 1632    14854223  2195 - 563 = 1632    14874330  2264 - 590 = 1674    15404331  2265 - 591 = 1674    15414332  2266 - 592 = 1674    1542`

So the answer is 1332 (S = 1; E = 3; N = 2); the decimal equivalent subtraction is 730 - 217 = 513, which matches the decimal conversion of the base-7 interpretation, 513.

FOR s = 1 TO 4
b8a = INT(8 ^ 3 + .5) * s
b5a = INT(5 ^ 3 + .5) * s
b7a = INT(7 ^ 3 + .5) * s
FOR e = 0 TO 4
IF e <> s THEN
b8b = b8a + INT(8 ^ 2 + 8 + .5) * e
b5b = b5a + INT(5 ^ 2 + 5 + .5) * e
b7b = b7a + INT(7 ^ 2 + 7 + .5) * e
FOR n = 0 TO 4
IF n <> s AND n <> e THEN
b8c = b8b + n
b5c = b5b + n
b7c = b7b + n
ct = ct + 1
seen\$ = LTRIM\$(STR\$(s)) + LTRIM\$(STR\$(e)) + LTRIM\$(STR\$(e)) + LTRIM\$(STR\$(n))
PRINT USING "##  &  #### - ### = ####    #### "; ct; seen\$; b8c; b5c; b8c - b5c; b7c;
IF b8c - b5c = b7c THEN
PRINT "<--"
ELSE
PRINT
END IF
END IF
NEXT
END IF
NEXT
NEXT

 Posted by Charlie on 2007-05-10 11:33:53

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