Henry Ernest Dudeney/Puzzles and Curious Problems/233 - The Nougat Puzzle/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $233$

A block of nougat is $16$ inches long, $8$ inches wide, and $7 \tfrac 1 2$ inches deep.

What is the greatest number of pieces that I can cut from it measuring $5$ inches by $3$ inches by $2 \tfrac 1 2$ inches?

$24$ pieces.

Cut off and throw away a piece $1$ inch thick off the end, leaving a block $15$ inches long.

Then cut the block into two pieces:

$15$ inches long, $5$ inches wide, and $7 \tfrac 1 2$ inches deep

$15$ inches long, $3$ inches wide, and $7 \tfrac 1 2$ inches deep.

The former can be cut into $15$ piece of nougat $5$ inches by $3$ inches by $2 \tfrac 1 2$ inches.

The latter can be cut into $9$ piece of nougat $5$ inches by $3$ inches by $2 \tfrac 1 2$ inches.

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