Henry Ernest Dudeney/Puzzles and Curious Problems/353 - The Three Sugar Basins/Solution
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Puzzles and Curious Problems by Henry Ernest Dudeney: $353$
- The Three Sugar Basins
- Three basins each contain the same number of lumps of sugar,
- and nine cups are empty.
- If we transfer to each cup one-eighteenth of the number of lumps that each basin contains,
- we then find that each basin holds $12$ more lumps than each of the cups.
- How many lumps are there in each basin before they are removed?
Solution
- $36$
Proof
Let $n$ be the number of lumps each basin contains before starting.
Each sugar bowl transfers a total of $9 \times \dfrac n {18} = \dfrac n 2$ lumps to the teacups.
So after this transaction, each sugar bowl contains $n - \dfrac n 2 = \dfrac n 2$ lumps.
Each teacup then contains a total of $3 \times \dfrac n {18} = \dfrac n 6$ lumps.
Hence:
- $\dfrac n 2 = \dfrac n 6 + 12$
which after algebra leads us to:
- $n = 36$
$\blacksquare$
Sources
- 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $353$. -- The Three Sugar Basins
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $255$. The Three Sugar Basins