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Self-Referential (Posted on 2010-07-29) Difficulty: 3 of 5
If you use the word "and" in naming numbers above 100, then, for example, 999 is named "nine hundred and ninety-nine". Considering this as four words, one of them hyphenated, the letter counts in the four words are 4, 7, 3 and 10. The product of these four numbers is 840.

There is one 3-digit number such that if you apply the above procedure, the final product of its four word lengths is the same as the original number. What is that number?

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Solution trial end error | Comment 3 of 5 |



A is number of hundreds  , 3,4,or 5 letters 
B is 21=7*3 (product of # of letters in "hundred and")
C is # of letters in the two last words (8,9,10  and 11) 

There are at most 15 possible results to be checked  from 3*21*8 to 5*21*11.

3*21*8=504     4*21*5=420

3*21*9=567     4*21*10=840

3*21*10=630     3*21*6=378

3*21*11=693     3*21*11=693   answer  STOP


  Posted by Ady TZIDON on 2010-07-29 19:17:51
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