Henry Ernest Dudeney/Puzzles and Curious Problems/197 - Economical Dissection/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $197$

Economical Dissection

Take a block of wood $8$ units long by $4$ units wide by $3 \tfrac 3 4$ units deep.

How many pieces, each measuring $2 \tfrac 1 2$ by $1 \tfrac 1 2$ by $1 \tfrac 1 4$ can be cut out of it?

Solution

Even though the volume of the block is enough to make $25$ pieces, you can in fact make only $24$.

Reduce the length of the block by half a unit.

The smaller piece off the end cannot be used.

Then cut the larger piece into $3$ slabs, each $1 \tfrac 1 4$ units thick.

Eight blocks can then be cut from each slab.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $197$. -- Economical Dissection