Charlie, Alison, and Abi want to buy some sweets at the cinema. Sweets cost 32p, and they all have exactly the right amount.
Charlie has 3 coins:
20p, 10p, 2p.
Alison has 7 coins:
10p, 5p, 5p, 5p, 5p, 1p, 1p.
Abi has 32 coins. We're not going to list them, we expect you'll be able to work out what she has!
Is there a way of making 32p with 4 coins? How about 5 coins?
Or ANY number of coins between 3 and 32?
Explore ways of making other totals using different numbers of coins.
Is it always possible to make a total using every number of coins between the minimum and the maximum?
Comments
A trip to the Cinema
10p 10p 10p 2p
10p 10p 10p 1p 1p
10p 10p 5p 5p 1p 1p
10p 5p 5p 5p 5p 1p 1p
5p 5p 5p 5p 5p 5p 1p 1p
10p 5p 5p 5p 2p 2p 1p 1p 1p
5p 5p 5p 5p 5p 2p 2p 1p 1p 1p
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Re: A trip to the Cinema
Well done Abbey, this is a good start!
Can you describe the changes that you've made at each stage to increase the number of coins by 1?
Can you use these same manoeuvres to keep increasing the number of coins by 1 each time? Will you be able to keep going until you reach the combination that uses 32 coins?
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Maths
Following on from Abbey, here are solutions for 3 coins to 32 coins:
3 - 20,10,2
4 - 10,10,10,2
5 - 10,10,10,1,1
6 - 10,5,5,5,5,2
7 - 5,5,5,5,1,1,10
8 - 5,5,5,5,5,5,1,1
10 - 5,5,10,2,2,2,2,2,1,1
11 - 2,2,1,5,5,5,5,2,2,1,2
12 - 2,2,2,2,2,5,5,5,2,2,2,1
13 - 1,1,2,2,2,2,5,5,5,2,2,2,1
14 - 1,1,1,1,10,1,1,1,1,1,1,1,1,10
15 - 1,1,1,1,5,5,1,1,1,1,1,1,1,1,10
16 - 16 x 2
17 - 15 x 2, 2 x 1
18 - 14 x 2, 4 x 1
19 - 13 x 2, 6 x 1
20 - 12 x 2, 8 x 1
21 - 11 x 2, 10 x 1
22 - 10 x 2, 12 x 1
23 - 9 x 2, 14 x 1
24 - 8 x 2, 16 x 1
25 - 7 x 2, 18 x 1
26 - 6 x 2, 20 x 1
27 - 5 x 2, 22 x 1
28 - 4 x 2, 24 x 1
29 - 3 x 2, 26 x 1
30 - 2 x 2, 28 x 1
31 - 1 x 2, 30 x 1
32 - 32 x 1
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Maths
Well done, Katie!
Can you use these manoeuvres to make a total other than 32 with different numbers of coins? Are there totals for which some numbers of coins don't work?
If the total gets very large, it can take a long time to list the solutions. Could you describe an algorithm that would generate a solution for each number of coins for a given total?
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maths
The answer for Abi's coins are
32 one penny coins
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a trip to the cinema
5, 5, 5, 5, 5, 2, 2, 2, 1
5, 5, 5, 5, 5, 5, 2
20, 5, 2, 1, 2, 1, 1
10, 10, 10, 2
10, 2, 5, 10, 5
20, 5, 5, 1, 1
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