Dudeney’s Classical Money Puzzles
Edwardian arithmetic has a certain gravity to it. Coins were counted by hand, ratios were trusted, and every penny had a place. The puzzles below preserve that spirit — each question stated as originally posed, each answer reduced to its bare numerical truth.
1. A Post-Office Perplexity
A crown is laid down for twopenny stamps, six times as many penny stamps,
and the remainder in twopence-halfpenny stamps.
- 5 twopenny stamps
- 30 penny stamps
- 8 twopence-halfpenny stamps
\[
5\times2d + 30\times1d + 8\times2.5d = 60d
\]
2. Youthful Precocity
Sixteen dozen dozen bananas are sold under a curious sixpence condition.
What did Fred pay for one banana?
\[
16\times12\times12 = 2304 \text{ bananas}
\]
The unit price simplifies to 1¼d per banana.
3. At a Cattle Market
Three men exchange animals so that each proposed trade leaves the receiver
with a fixed multiple of the giver’s stock.
- Hodge: 29 animals
- Jakes: 11 animals
- Durrant: 23 animals
4. The Beanfeast Puzzle
Cobblers, tailors, hatters, and glovers spend £6 13s under strict ratio rules.
- Cobblers: £1 10s
- Tailors: £1 17s 6d
- Hatters: £2 10s
- Glovers: 15s 6d
5. A Queer Coincidence
Seven players each win once, doubling every other man’s money.
Original holdings (in pence):
\[
1,\;2,\;4,\;8,\;16,\;32,\;64
\]
All finish with 32d (2s 8d).
6. A Charitable Bequest
Each year 55s is given out under fixed payments to men and women.
The Diophantine equation admits 11 distinct solutions.
Hence the charity lasts for 11 years.
7. The Widow’s Legacy
£8,000 is divided among a widow, five sons, and four daughters by fixed ratios.
\[
39M = 8000 \Rightarrow M = \frac{8000}{39}
\]
Widow’s share: £205 2s 1d.
8. Indiscriminate Charity
Three beggars are paid successively, each receiving more than half the remainder.
Working backwards gives an initial sum of 31d (2s 7d).
9. The Two Aeroplanes
Two machines sell for £600 each — one at a loss, one at a profit.
Total cost £1,250; total return £1,200.
Overall loss: £50.
Overall loss: £50.
10. Buying Presents
Money leaves pounds and returns as shillings — and vice versa.
He spent £5 5s.
11. The Cyclists’ Feast
Two cyclists depart, raising the bill for those who remain.
Originally there were 10 cyclists.
12. A Queer Thing in Money
An amount in £-s-d using one repeated digit with matching digit sums.
The other amount is £33 3s 3d.
13. A New Money Puzzle
Use the digits 1–9 once each to form the smallest £-s-d-q sum.
Minimum achieved by £1 2s 3¼d.
14. Square Money
Find amounts whose sum equals their product.
After 2d and 2d, the next pair is 3d and 6d.
15. Pocket Money
Largest silver sum that cannot make change for 10s.
£1 1s 10d.
16. The Millionaire’s Perplexity
Distribute $1,000,000 using only $1 and powers of 7.
A valid distribution exists using six of each power.
17. The Puzzling Money-Boxes
Four boxes, six coins total, sum 45s — yet become equal after operations.
Coins used: one sovereign, two half-sovereigns,
two florins, and one shilling.
18. The Market Women
Each woman receives 2s 2½d at a distinct price per pound.
Maximum possible: 17 women.
19. The New Year’s Eve Suppers
Singles and couples dine to a precise total of £5.
5 single ladies, 10 single men, 5 couples.
20. Beef and Sausages
Equal weights versus equal money spent.
Total spend: £1 4s 6d.
21. A Deal in Apples
Two free apples reduce the price per dozen by 1d.
He receives 16 apples for 1s.
22. A Deal in Eggs
Three prices, 100 eggs, equal numbers of two kinds.
8 at 5d, 28 at 1d, 64 at ½d.
23. The Christmas-Boxes
100 silver coins, equal gifts, total 361d.
A specific mixed-coin solution exists, as given by Dudeney.
24. A Shopping Perplexity
Two ladies each need six coins — alone or together.
Smallest pair:
3s 4½d and 1s 7½d.
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