# Solution

(related to Problem: Simple Division)

Subtract every number in turn from every other number, and we get $358$ (twice), $716,$ $1,611,$ $1,253,$ and $895.$ Now, we see at a glance that, as $358$ equals $2 \times 179,$ the only number that can divide in every case without a remainder will be $179.$ On trial, we find that this is such a divisor. Therefore, $179$ is the divisor we want, which always leaves a remainder $164$ in the case of the original numbers given.

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### References

#### Project Gutenberg

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

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