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Humanising Language Teaching
Year 1; Issue 5; August 1999

An Old Exercise

Deduction Puzzles

Challenge to Think (Christine Frank et al, l983) has just been consigned to the knackers' yard by OUP and so it feels sensible to offer you one of its most intriguing exercise types in this corner of HLT dedicated to hoary, dusty old things!

Deduction Puzzles are easy to use and are particularly handy if you are teaching a mixed bag of conditionals to an intermediate class.

Simply pair the students and give them the worksheet that follows. Ask them to read the story and then ask each other the questions alternately: student A asks questions 1 and B answers it, then B asks question 2 and A answers it etc…. till they triumphantly find the solution.

Get early finishers to help the students who are at sea and cannot find the solution.

When you have read through the story and questions below you may panic: "What is the answer, I can't work it out."

You don't have to, as there are always students in the class who love logical mathematical thinking and will slice through the puzzle. For them it may well be too simple.


A sultan ordered ten goldsmiths to make ten coins each. Each coin was to weigh exactly ten grams of pure gold. One of the goldsmiths was a bad man. He decided to cheat. He made all his ten coins one gram short. Now the sultan heard that one of the goldsmiths had cheated. He also heard that this man had made each of his coins one gram short.

The sultan was a very clever person. He took a certain number of coins from each of the smiths, weighed them together once only and found their weight to be 540 grams. This was enough for him to find out which one of the smiths had cheated.

Who was the cheat and how did the sultan find him?

  1. How many goldsmiths were there?

  2. How many of them were cheats?

  3. The cheat, like the others, made ten coins. How many grams short was each coin?

  4. Did the sultan find the cheat

    1. by looking each man in the eye
    2. by weighing coins
    3. by asking his mother?

  5. How many times did he weigh the coins he took from them?

  6. Did he take the coins to weigh from

    1. one goldsmith
    2. some goldsmiths
    3. all of them?

  7. Suppose he had taken all ten coins from each smith and put them together on the scales. When he weighed them how many grams short would they have been?

  8. Would he have known that one of the smiths had cheated?

  9. Would he have known which smith had cheated?

  10. Supposing he took one coin from the first smith, two coins from the second, and three from the third, how many would he take from the others?

  11. How many coins would that be altogether?

  12. If nobody had cheated, what should the total weight of these coins have been?

    1. 500 grams
    2. 550 grams
    3. 600 grams?

  13. How much did the coins he put on the scale actually weigh?

  14. So how many of the coins on the scale were made by the cheat?

  15. Who was the cheat?

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