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In order to generate more traffic on this blog, I thought I’d occasionally introduce a puzzle for you to work on.

The first puzzle.

Nine digits, other than zero, can be arranged uniquely to form four numbers which are all squares:-

 9 (32) 81 (92) 324 (182) 576 (242)

What is the smallest possible square number comprising all nine digits together, and the largest square number comprising all nine digits together?

– The Vedic Maths Forum India

#### 5 COMMENTS

1. Should the squares use the numbers 1 through 9 just once? In other words, should each of the answers sought be exactly 9 digits long?

2. Correct on both counts. Exactly nine digits long. Each digit may only be used once. Needless to say, the digit zero is not used in this puzzle.

3. Should I just post the answers here or should I email them to you? I don't want to be a spoiler by posting the answers in the comments for everyone to see.

4. OK. The answers are 139,854,276 and 923,187,456. The first is 11826^2, and the second number is 30384^2.