Solution

(related to Problem: A Packing Puzzle)

On the side of the box, $14$ by $22 \frac 45,$ we can arrange $13$ rows containing alternately $7$ and $6$ balls, or $85$ in all. Above this, we can place another layer consisting of $12$ rows of $7$ and $6$ alternately, or a total of $78.$ In the length of $24\frac{9}{10}$ inches $15$ such layers may be packed, the alternate layers containing $85$ and $78$ balls. Thus $8$ times $85$ added to $7$ times $78$ gives us $1,226$ for the full contents of the box.

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References

Project Gutenberg

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

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