I am thinking of a 5 digit number that when tripled is a perfect square.

Also, when the 5 digit number is split, the first number is double the second one. What is the five digit number?

(Splitting the 5 digit number into two numbers means 12345 into 1 and 2345 or 123 and 45.)

(In reply to Puzzle Solution by K Sengupta)

We know that by the very definition a five digit number cannot admit of leading zeroes, unless stated overtly in the given problem.

However, if for argument's sake we assume that the number admits of leading zeroes, then we observe that abcde = 00000 is a trivial solution.

With a=0, we now consider the possible cases like:

(i) bc = 2*de, (ii) bc = 2*e, (iii) c = 2*e, ......... etc., and verify which of these are in conformity with the given conditions.

After going through all the possible cases, we observe that only cd = 2*e, for b = 0 in conjunction with abcde = 3*(x^2) yields a valid solution, and that is: abcde = 00147

Thus, 00000 and 00147 are the only additional solutions if we assume leading zeroes.

Posted by K Sengupta on 2008-05-19 04:54:07