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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?

See The Solution Submitted by Charlie    
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Solution trial end error | Comment 3 of 5 |

sol:

p=A*B*C

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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