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Substitute seen, get result (Posted on 2007-05-10) Difficulty: 3 of 5
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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Solution 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             b7
1002   514 - 127 =  387     345
1003   515 - 128 =  387     346
1004   516 - 129 =  387     347
1220   656 - 185 =  471     455
1223   659 - 188 =  471     458
1224   660 - 189 =  471     459
1330   728 - 215 =  513     511
1332   730 - 217 =  513     513 <--
1334   732 - 219 =  513     515
1440   800 - 245 =  555     567
1442   802 - 247 =  555     569
1443   803 - 248 =  555     570
2001  1025 - 251 =  774     687
2003  1027 - 253 =  774     689
2004  1028 - 254 =  774     690
2110  1096 - 280 =  816     742
2113  1099 - 283 =  816     745
2114  1100 - 284 =  816     746
2330  1240 - 340 =  900     854
2331  1241 - 341 =  900     855
2334  1244 - 344 =  900     858
2440  1312 - 370 =  942     910
2441  1313 - 371 =  942     911
2443  1315 - 373 =  942     913
3001  1537 - 376 = 1161    1030
3002  1538 - 377 = 1161    1031
3004  1540 - 379 = 1161    1033
3110  1608 - 405 = 1203    1085
3112  1610 - 407 = 1203    1087
3114  1612 - 409 = 1203    1089
3220  1680 - 435 = 1245    1141
3221  1681 - 436 = 1245    1142
3224  1684 - 439 = 1245    1145
3440  1824 - 495 = 1329    1253
3441  1825 - 496 = 1329    1254
3442  1826 - 497 = 1329    1255
4001  2049 - 501 = 1548    1373
4002  2050 - 502 = 1548    1374
4003  2051 - 503 = 1548    1375
4110  2120 - 530 = 1590    1428
4112  2122 - 532 = 1590    1430
4113  2123 - 533 = 1590    1431
4220  2192 - 560 = 1632    1484
4221  2193 - 561 = 1632    1485
4223  2195 - 563 = 1632    1487
4330  2264 - 590 = 1674    1540
4331  2265 - 591 = 1674    1541
4332  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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