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129 digits (Posted on 2010-06-18) Difficulty: 4 of 5
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FIND/EXTRA=quarter?

No Solution Yet Submitted by Ady TZIDON    
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some thoughts and solutions | Comment 1 of 6
on initial inspection this can not be treated as a straight crytarithm as find has fewer digits than extra, the division will be less than 1 and thus not an integer in any base.  Also if you treat the word quarter as part of the crytarithm then there are 11 different letters and thus must be at least in base 12.  So there must be a different way to interpret this.  My first thought was quarter = 1/4 and that we are to solve
FIND/EXTRA = 1/4
for this I found the following 34 solutions
Solution #1: 2637/10548 = 1/4

Solution #2: 3627/14508 = 1/4

Solution #3: 3762/15048 = 1/4

Solution #4: 5184/20736 = 1/4

Solution #5: 7542/30168 = 1/4

Solution #6: 2594/10376 = 1/4

Solution #7: 3926/15704 = 1/4

Solution #8: 4259/17036 = 1/4

Solution #9: 4763/19052 = 1/4

Solution #10: 9254/37016 = 1/4

Solution #11: 2596/10384 = 1/4

Solution #12: 9526/38104 = 1/4

Solution #13: 4758/19032 = 1/4

Solution #14: 7548/30192 = 1/4

Solution #15: 9285/37140 = 1/4

Solution #16: 7091/28364 = 1/4

Solution #17: 7109/28436 = 1/4

Solution #18: 9071/36284 = 1/4

Solution #19: 9107/36428 = 1/4

Solution #20: 3907/15628 = 1/4

Solution #21: 7039/28156 = 1/4

Solution #22: 9127/36508 = 1/4

Solution #23: 5196/20784 = 1/4

Solution #24: 6195/24780 = 1/4

Solution #25: 6951/27804 = 1/4

Solution #26: 3695/14780 = 1/4

Solution #27: 8519/34076 = 1/4

Solution #28: 9185/36740 = 1/4

Solution #29: 7648/30592 = 1/4

Solution #30: 8926/35704 = 1/4

Solution #31: 3942/15768 = 1/4

Solution #32: 4392/17568 = 1/4

Solution #33: 5796/23184 = 1/4

Solution #34: 7956/31824 = 1/4

another interpretation is that you are to solve
4*FIND = EXTRA
where 4 is not used anywhere in FIND or EXTRA.
This narrows down the solutions to the following 3
Solution #1: 3907/15628 = 1/4

Solution #2: 7039/28156 = 1/4

Solution #3: 9127/36508 = 1/4

my gut tells me the intended solution is unique, so I am still looking for a way to interpret it such that there is a unique solution

  Posted by Daniel on 2010-06-18 16:55:09
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