Henry Ernest Dudeney/Puzzles and Curious Problems/160 - Boxes of Cordite

Puzzles and Curious Problems by Henry Ernest Dudeney: $160$

Cordite charges for $6$-inch howitzers were served out from ammunition dumps in boxes of $15$, $18$ and $20$.

"Why the three different sizes of boxes?" I asked the officer on the dump.

He answered: "So that we can give any battery the number of charges it needs without breaking a box.

This was an excellent system for the delivery of a large number of boxes,

but failed in small cases, like $5$, $10$, $25$ and $61$.

Now, what is the biggest number of charges that cannot be served out in whole boxes of $15$, $18$ and $20$?

It is not a very large number.

Dudeney reports that this puzzle is the work of one W. H.-J., but it is not apparent who that person is.

When the collection was edited for its $1968$ re-publication, the presentation of these initials was changed to W. H. J.

1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $160$. -- Boxes of Cordite
1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $227$. Boxes of Cordite