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Awesome Level (Posted on 2012-09-15) Difficulty: 3 of 5
Assuming that none of the numbers contain any leading zero, it can be observed that none of the alphametics: LEVEL+LEVEL = AWESOME or, LEVEL+LEVEL+LEVEL = AWESOME possess any solution. In other words, when LEVEL is added twice (or thrice), it does not equal AWESOME. (Each of the capital letters denotes a different base ten digit from 0 to 9)

(i) What are the respective minimum and maximum number of times that LEVEL can be added to make AWESOME?

(ii) What further solutions are there for (i), assuming that the numbers can contain leading zeroes? Of these additional answers, what are the respective minimum and maximum number of times that LEVEL can be added?

No Solution Yet Submitted by K Sengupta    
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Solution part 1 computer solution Comment 2 of 2 |

DEFDBL A-Z
FOR num = 11 TO 900
  FOR l = 1 TO 9
    FOR e = 0 TO 9
      IF e <> l THEN
        FOR v = 0 TO 9
          IF v <> e AND v <> l THEN
            used$ = LTRIM$(STR$(l)) + LTRIM$(STR$(e)) + LTRIM$(STR$(v))
            level = 10001 * l + 1010 * e + 100 * v
            prod = num * level
            p$ = LTRIM$(STR$(prod))
            IF LEN(p$) = 7 THEN
              good = 1
              FOR i = 1 TO 7
                d$ = MID$(p$, i, 1)
                dig = VAL(d$)
                SELECT CASE i
                  CASE 3, 7
                    IF dig <> e THEN good = 0: EXIT FOR
                  CASE ELSE
                    IF INSTR(used$, d$) > 0 THEN good = 0: EXIT FOR
                    used$ = used$ + d$
                END SELECT
              NEXT
              IF good THEN PRINT num, level; prod
            END IF
          END IF
        NEXT
      END IF
    NEXT
  NEXT
NEXT

finds

multiple
of LEVEL         LEVEL  AWESOME
   37            48284  1786508
   42            24942  1047564
   49            64246  3148054
   59            91819  5417321
   75            35453  2658975
   83            97279  8074157
   112           74547  8349264
   126           72427  9125802
   127           62426  7928102
   142           24942  3541764
   144           32823  4726512
   153           26562  4063986
   155           15851  2456905
   155           40704  6309120
   169           46564  7869316
   174           32923  5728602
   176           16861  2967536
   194           14641  2840354
   275           15851  4359025
   279           19691  5493789
   338           18581  6280378
   445           15851  7053695
   525           15351  8059275
   575           15051  8654325
   575           15751  9056825

The minimum number is 37 and the maximum is 575. To be clear, the number of additions is between 36 and 574, as there is one more occurrence of LEVEL than the number of addition operations.  


  Posted by Charlie on 2012-09-15 16:17:03
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