Henry Ernest Dudeney/Puzzles and Curious Problems/229 - Geometrical Progression
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Puzzles and Curious Problems by Henry Ernest Dudeney: $229$
- Geometrical Progression
- Write out a series of whole numbers in geometrical progression, starting from $1$,
- so that the numbers should add up to a square.
- Thus, $1 + 2 + 4 + 8 + 16 + 32 = 63$.
- But this is one short of being a square.
- I am only aware of two answers in whole numbers, and these will be found easy to discover.
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Sources
- 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Geometrical Problems: Various Geometrical Puzzles: $229$. -- Geometrical Progression
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $243$. Geometrical Progression