 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Awesome Level (Posted on 2012-09-15) 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 No Rating Comments: ( Back to comment list | You must be logged in to post comments.) 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

`multipleof 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 Please log in:

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