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25. Figure It Out

We're looking for a 5-digit number where the sum of the 3rd and 5th digits is one less then the 4th, the 4th digit is double the 2nd, the 2nd digit is double the 1st, the 5th is 5 more than the 3rd and the 4th is the product of the 1st and 2nd. Can you find the number?
 

Scroll down the page for the answer.


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

If the number is given by the digits abcde then the information gives rise to 5 equations:

1.  c + e = d - 1
2.  d = 2b
3.  b = 2a
4.  e = c + 5
5.  d = ab

from 2 and 5:  2b = ab
so  a = 2

from 3:  b = 4

from 5:  d = 8

from 1:  c + e = 7

and from 4:  e = c + 5
so  c + (c + 5) = 7
so  c = 1

and the number is 24186
 

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