Saturday, 30 July 2016

Quibans 35: Copper coins

From the Daily Telegraph:

Disgruntled parent pays £60 school attendance fine for taking child on holiday in pennies

After taking his son out of school for a holiday, this man received a £60 fine from local authorities.

Rather than take the easy route, he changed £60 in cash into 1 and 2 pence pieces and proceeded to pour them over the reception desk of the local council office.

This story gives some quick and interesting Quibans opportunities.  Here are some ideas:
1) If he used 4,724 coins, how many 1p coins and how many 2p coins were there?
2) What is the smallest number of coins he could have used?
3) What is the biggest number of coins he could have used?
4) If we know the number of coins, how can we easily work out how many were 1p or 2p?
5) Is it possible to carry £60 worth of 1 and 2 pence pieces?
6) What was the weight of the coins?
7) If the coins were stacked up, how high would the stack be?

Answers and other information:
1) I prefer to answer questions 2, 3 and 4 first and then come back to this one.  I think it is still worth asking this question first, though.  
2) 3000 x 2p = 6000 pence.  It says that 1p coins were used too, so presumably 3001 is the smallest number of coins that could have been used.  (2999 x 2p and 2 x 1p)
3) 6000 x 1p = 6000 pence.  2p coins were used so 5999 coins is the biggest (5998 x 1p and 1 x 2p)
4)  There must be at least 3000 coins (that would be all 2 pence pieces).  Then, every time we change a 2p into two 1p coins we get an extra coin.  
Start with the number of coins and subtract 3000 from it.  This excess is the number of 2p coins that have been changed into 1p coins.  We need to double that number to find the number of 1p coins and subtract it from 3000 to find the number of 2p coins.  Not easy to get your head around (but it is possible to simplify this if you use algebra).
1) 4724 - 3000 = 1724.  This is the number of 2p coins that have been changed into 1p coins.
That leaves 3000 - 1724 = 1276 coins that are 2p.
1724 x 2 = 3448, which gives us 3448 1p coins.  Check that the number of coins adds up to 4724 and that the value makes £60.
5) It feels like it probably will.  60 pound coins would be fine, as would 120 50p coins.  Probably won't be good for your trouser pockets, though.  The source for the article (see below) includes a video of him emptying out the coins. 
6) This is rather neat.  A 1p coin weighs 3.56g and a 2p coin is double that, at 7.12g.  It doesn't matter how the coins are distributed between 1p and 2p - the weight will always be 6000 x 3.56g = 21.36kg
7) This is less straightforward for two reasons.  A 1p coin is either 1.52mm or 1.65mm thick (depending on the date and the composition of the metal used) and a 2p coin is either 1.85mm or 2.03mm thick.  The weights are in the ratio 1:2, so the thicknesses are not.  This means that two 1p coins are thicker than one 2p coin.  
If we assume there are the same number of 2p coins as 1p coins (this could be another question!) then there are 2000 1p coins and 2000 2p coins.  Using 1.9mm and 1.6mm as the thickness of each coin that would give a height of 7 metres.  Good luck with building that!


Sunday, 10 July 2016

Quibans 34: It's May v Leadsom

May v Leadsom to be next prime minister

From the BBC:

Theresa May and Andrea Leadsom will battle it out to become the next leader of the Conservative Party after Michael Gove was eliminated from the contest.
After the second MPs' ballot, Home Secretary Mrs May finished with 199 votes, Energy Minister Mrs Leadsom 84 and Mr Gove, the justice secretary, 46.
Conservative members will now decide the winning candidate, with the result due on 9 September.
The winner will become the UK's second female prime minister.

Possible questions:
1)            What percentage of the vote did each of them get?
2)            Let’s imagine that Michael Gove came second.  How many of Theresa May’s supporters would have needed to switch to Gove for that to happen?
3)            Let’s imagine that Michael Gove came second.  How many of Andrea Leadsom’s supporters would have needed to switch to Gove for that to happen?
4)            What is the biggest number of votes you could get and still come last?


Quibans 85: Crime and Police figures

From the Cambridge News: Violent crime in Cambridge has nearly doubled in a decade as police numbers drop 9 APR 2018 Bottom of For...