5-digit Number Puzzle - Solution
The Puzzle:
If we put the numeral 1 at the beginning, we get a number three times smaller than if we put the numeral 1 at the end of the number.
Our Solution:We can make an equation:
3(100000 + x) = 10x+1
(Why? Well, adding 100000 puts a 1 at the front of a five-digit number, and multiplying by 10 and adding 1 puts a 1 at the end of a number)
Solving this gives:
10x+1 = 3(100000 + x)
10x+1 = 300000 + 3x
10x = 299999 + 3x
7x = 299999
x = 299999/7 = 42857
The answer is 42857 (142857 is three times smaller than 428571)
3(100000 + x) = 10x+1
(Why? Well, adding 100000 puts a 1 at the front of a five-digit number, and multiplying by 10 and adding 1 puts a 1 at the end of a number)
Solving this gives:
10x+1 = 3(100000 + x)
10x+1 = 300000 + 3x
10x = 299999 + 3x
7x = 299999
x = 299999/7 = 42857
The answer is 42857 (142857 is three times smaller than 428571)