MATHS PUZZLE # 5 FIRST LEG (Second Year)

(from the 1^st to the 8^th of November)

The digit on the left of a six-digit number is 1. Moving this 1 to the other extreme, the number is three times higher than the first number.

What is the original number?

You can send the solution to FernandoEscuin@iescampanar.com 

SOLUTION

 

1abcde x  3 = abcde1   ð    3e finishes  in 1       ð    e = 7

1abcd7 x 3 = abcd71    ð    3d+2 finishes in 7    ð    3d finishes in 5   ð  d=5

1abc57 x 3 = abc571    ð    3c + 1 finishes in 5  ð    3c finishes in 4   ð  c=8

1ab857 x 3 = ab6571   ð    3b+2 finishes in 8    ð    3b finishes in 6   ð  b=2

1a2857 x 3 = a28571   ð    3a finishes in   2      ð    a = 4

The number is 142857

SOLVED IN A DIFFERENT FORM:

3(100.000 + x ) = 10x +1

300.000 + 3x = 10x + 1

299.999 = 7x

x = 42857

The number is 142857