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Not All There
Programme Outline
A giant combination lock stands between the Guard and his lunch. The combination is a two-place decimal, and the lock (which has a mind of its own) announces whether a guessed combination is too high or too low. By exploring how many combinations are left after each guess, Lisa and the Guard demonstrate the relationship between fractions and decimals.
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Start to 04:25 - Introduction
The Guard introduces his new combination lock, which has been fitted to his hut. Lisa works out that the buttons (marked as fractions) alter the corresponding places in the lock's decimal display. She tries a couple of numbers, but they're too small, and the lock reveals that it will only allow ten attempts to find the combinations. |
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04:25 to 05:48 - Impossible!
Lisa works out how many combinations there could be: 1000 possibilities. She concludes that she'll never find the right combination. The Wizard appears, and gives Lisa a vital clue - the lock is telling her which combinations she can ignore. |
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05:48 to 06:45 - The Mathematical Encyclopaedia
The Encyclopaedia opens to page 'three hundred and sixty-five and a bit', and goes on to explain why the number of days in the year isn't a whole number, and what we do about it. Because of the system of leap years, the year averages out at 365.2422 days. |
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06:45 to 09:45 - Back to the problem
Lisa makes a scale for all the possible combinations; as she guesses them, the Guard paints out all the numbers which can no longer be correct. For example, Lisa starts by guessing that the combination could be 5.00, which the lock says is too low. The Guard can therefore paint out the lower half of the scale, leaving just the combinations between 5.00 and 9.99. Lisa's next guess is 7.50 (too large), then 6.25 (too small). |
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09:45 to 10:10 - Working out the remaining combinations
From his scale, the Guard can see that only an eighth of the initial combinations could still be right. That means there are only 125 possible combinations left to search - but they have just seven guesses left. Is that sufficient? |
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10:10 to 11:00 - Percentages and fractions
The Wizard describes how fractions can be used to fill in the gaps between whole numbers. He goes on to explain the equivalence of percentages and hundredths, then simplifies such a fraction to allow him to do a calculation easily. |
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11:00 to End - Cracking the combination
Lisa and the Guard finally crack the combination on their last try, and with great reluctance the diabolical machine unlocks the Guard's hut. At last, his lunch is free! |
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