self Maths Puzzle

Find a 6-digit integer abcdef with the following properties:

Take the rightmost digit and place it in front of the integer to form a new number (abcdef --> fabcde).

The new one is the product of the old one and the shifted digit (fabcde = f*abcdef).

What was the original integer?

Read Solution (Total 1)

a=1 b=0 c=2 d=5 e=6 f=4

fabcde = f x abcdef

410256 = 4 x 102564
12 years agoHelpfull: Yes(2) No(0)

self Other Question

find 3 consecutive odd integers, all less than 100, such that the sum of their squares forms a Unidigit (that is, all its digits are the same). Thus, for integer abc, a^2 + b^2 +c^2 equals a Unidigital. A right-angled triangle whose sides are all integers has a perimeter which is a perfect square and an area which is a perfect cube. Find the sides, perimeter, and area of the smallest possible solution.