All ten digits

Logic Level 4

If we square a 5 digit integer $\overline{PQQQQ}$ less than 90000, it will be 1 more than a 10-digit integer which contains each of the digits 0, 1, 2, ... , 9. What is this 5 digit integer?

The answer is 85555.

1 solution

Kenny Lau
Jul 22, 2015

Actually there are two solutions: $85555^2=7319658024+1$ and $97777^2=9560341728+1$ .

I used a java program to generate all squares of such form and looked at them one by one. It was not a tedious task since there is only $90$ entries.

The code and the list generated is here: http://pastebin.com/N959TE5u

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The number is less than 9000. So only one of these solutions is valid.

Harshita Sahijwani - 5 years, 10 months ago

Haha I wrote that before the question was modified.

Kenny Lau - 5 years, 10 months ago

All ten digits

The answer is 85555.

1 solution

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