Problem: The Torn Number

I had the other day in my possession a label bearing the number $3025$ in large figures. This got accidentally torn in half, so that $30$ was on one piece and $25$ on the other, as shown in the illustration.

q113

On looking at these pieces I began to make a calculation, scarcely conscious of what I was doing when I discovered this little peculiarity. If we add the $3$ and the $25$ together and square the sum we get as the result the complete original number on the label! Thus, $30$ added to $25$ is $55,$ and $55$ multiplied by $55$ is $3025.$ Curious, is it not? Now, the puzzle is to find another number, composed of four figures, all different, which may be divided in the middle and produce the same result.

Solutions: 1


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References

Project Gutenberg

  1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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