Henry Ernest Dudeney/Modern Puzzles/143 - The Stone Pedestal/Solution
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Modern Puzzles by Henry Ernest Dudeney: $143$
- The Stone Pedestal
- In laying the base and cubic pedestal for a certain public memorial,
- There was exactly the same number of these blocks (all uncut) in the pedestal as in the square base on the centre of which it stood.
- Look at the sketch and try to determine the total number of blocks actually used.
- The base is only a single block in depth.
Solution
- $1458$ blocks.
Proof
Ridiculously messy question.
Let $2 x$ be the number of blocks used in total.
Then we have that $x$ are used in the base and $x$ are used in the pedestal.
Let $y$ be the number of blocks on along one edge of the pedestal.
We have that:
- $x = y^3$
It looks as though the length of one side of the base is $3$ times the length of one edge of the pedestal.
On that assumption, we have that:
\(\ds \paren {3 y}^2\) | \(=\) | \(\ds y^3\) | ||||||||||||
\(\ds \leadsto \ \ \) | \(\ds y\) | \(=\) | \(\ds 9\) | |||||||||||
\(\ds \leadsto \ \ \) | \(\ds x\) | \(=\) | \(\ds y^3 = 729\) | |||||||||||
\(\ds \leadsto \ \ \) | \(\ds 2 x\) | \(=\) | \(\ds 1458\) |
$\blacksquare$
Sources
- 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $143$. -- The Stone Pedestal
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $314$. The Stone Pedestal