The first four puzzles involve coins from the old British currency. A pound is 20 shillings and a shilling is 12 pence. A half-sovereign is 10 shillings, a crown is 5 shillings, a double-florin is four shillings, a half-crown is 2 shillings and sixpence, a florin is 2 shillings. 3 2s. 6d. means three pounds, two shillings and six pence.

Xpress-Mosel models are available by clicking on Solution.

1. A tobacconist bought a quantity of pipes at 2s. 1d. each and others at 4s. 1d. each. He spent in all 8 6s. 8d. on the pipes. How many of each kind did he buy? (Clarke)    Solution

2. Tommy was given 15 coins for his birthday, all in half-crowns, shillings and sixpences. When he added it up he found that he had 1 5s. 6d. How many half-crowns was he given? (Clarke)    Solution

3. A man who possesses a half-sovereign, a florin and a sixpence goes into a shop and buys goods worth 7 shillings and 3 pence. But the shopkeeper cannot give him the correct change, as his coins are a crown, a shilling, and a penny. But a friend comes in the shop, and finds that he has a double-florin, a half-crown, a fourpenny piece and a threepenny bit.

Can the shopkeeper effect an exchange that will enable him to give the man the correct change, and to give his friend the exact equivalent of his coins? (Wakeling)    Solution

4. "Mrs Spooner called this morning," said the honest grocer to his assistant. "She wants twenty pounds of tea at 2s. 4 1/2d. per lb. Of course we have a good tea 2s. 6d. tea, a slightly inferior at 2s 3d., and a cheap Indian at 1s. 9d., but she is very particular always about her prices."

"What do you propose to do?" asked the innocent assistant.

"Do?" exclaimed the grocer. "Why, just mix up the three teas in different proportions so that the twenty pounds will work out fairly at the lady's price. Only don't put in more of the best tea than you can help, as we make less profit on that, and of course you will use only our complete pound packets. Don't do any weighing."

How was the poor fellow to mix the three teas? Could you have shown him how to do it? (Dudeney)    Solution

5. A butcher received an invoice for a consignment of 72 turkeys, but unfortunately it was smudged and a couple of figures were unreadable. All he could read was '-67.9-', with the first and last figures illegible. Nevertheless, being a 'rec.puzzler', he was able to work out the price of a turkey immediately. What was the price of a turkey? (rec.puzzles)    Solution

6. At a public-school camp five schools, Aldhouse, Bedminster, Chartry, Radford and Rugenham were represented. The smallest contingent from the five schools was greater than 20 but less than 30. Aldhouse sent two less than half of the Rugenham contingent. The Radford and Rugenham contingents together were 14 greater than the combined Bedminster and Chartry contingents. The Bedminster and Rugenham contingents together were two short of half the total complement from the five schools while the Chartry and Radford contingents combined mustered 13/32 of that total.

What was the strength of each contingent? (Clarke)    Solution

7. Place as few bishops as possible on an ordinary chessboard so that every square of the board shall be either occupied or attacked. (Dudeney)    Solution

8. What is the greatest number of bishops that can be placed on the chessboard without any bishop attacking another? (Dudeney)    Solution

9. How many queens are needed, and in what position, so that every unoccupied square of the chessboard is under direct attack from some queen? (Kraitchik)    Solution

10. Place eight queens on a chessboard in such a way that none of the queens is attacking another queen. (Schuh)    Solution

11. The Amazons.

Remove three of the queens to other squares so that there shall be eleven squares on the board that are not attacked. The removal of the three queens need not be by "queen moves". You may take them up and place them anywhere. There is only one solution. (Dudeney)    Solution

12. Joshua is a biology student. His project for this term is measuring the effect of an increase in vitamin C in the diet of nine laboratory rats. Each rat will have a different diet supplement of 1 to 20 units. Fractions of a unit are not possible.

To get the maximum value for his experiment, Joshua has decided that for any group of three rats the supplements should not be in arithmetic progression. In other words, for three rats chosen at random, the biggest supplement less the middle supplement should be different from the middle supplement less the smallest supplement. Thus, if two of the supplements were 7 and 13 units, no rat could have a supplement of 1, 10 or 19 units.

Find a set of supplements that Joshua could use. (Sole)    Solution

Clarke, L.H., (1954), Fun with Figures, William Heinemann Ltd M
Dudeney, H.E., (1917), Amusements in Mathematics, Thomas Nelson and Sons.
Kraitchik, M., (1942), Mathematical Recreations, W.W. Norton and Company.
Schuh, F., (1943), Wonderlijke Problemen; Leerzam Tijdverdrijf Door Puzzle en Speel, W.J. Thieme & Cie, Zutphen.
Sole, T., (1988), The Ticket to Heaven and other Superior Puzzles, Penguin Books
Wakeling, E., (1995), Rediscovered Lewis Carroll Puzzles, Dover.

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