Tag Archives: Biased coin

January 2015 News

Happy New Year! Best wishes for twenty-fifteen, or two thousand and fifteen or ‘two oh one five’. Which is the correct way to say the year? Well it certainly is not the third suggestion above. More about that later.

One of my Christmas presents this year was the book “Are you smart enough to work at Google”. It’s an excellent read for anyone interested in logic puzzles and a diverse range of other topics which have been used as interview questions for prospective Google employees. I’ll use one of the mathematically related questions as the puzzle for this newsletter:

“You’re playing football on a desert island and want to toss a coin to decide the advantage. Unfortunately, the only coin on the island is bent and is seriously biased. How can you use the biased coin to make a fair decision?”

The answer is at the end of this newsletter.

Thanks as always for the comments received last month. One in particular from Alan Ramm about the Starter for 16th December which asks pupils for a power of three and a power of two which are consecutive numbers. The surprising result is that there are four different answers where both numbers are less than ten. Alan informs us that this leads to Catalan’s conjecture, first stated in 1844 but not proved until 2002. It is explained nicely on Wikipedia but is a little beyond the scope of school Mathematics!

December was a busy month for updating pages on the Transum website there were also a number of new activities added including Christmas Consonants, Christmas Toggle Tree, Christmas Tree Trim, Set Notation Matching, Pu Wiang, Pong Hau K’l and Cat Face.

Questions in my mind at the moment are about Christmas Toggle Tree. I have never seen a puzzle like this before and I’m really interested to hear what strategies people will use to do it. As yet I have not come up with an elegant method but sure someone out there can. I’m also wondering whether we have finally found the minimum number of moved required to do Pu Wiang. I thought I had the answer until Colleen Young’s (@ColleenYoung) and her colleague, Elaine, found a more efficient solution. The record currently stands at 19 moves but I need an insightful mathematician to prove this is indeed the minimum number of moves required.

Now to the pronunciation of the year question. The aspect I’d like to examine is the use of ‘oh’ for nought or zero. For the whole of my teaching career I have told pupils that ‘oh’ is a letter that comes between n and p and it is not a number. But has common usage eroded this stance? For example how would you say the number associated with James Bond (007)?

The answer to these questions are clearly provided in a podcast I listen to called “Grammar Girl’s Quick and Dirty Tips” by Mignon Fogarty. She says the ‘oh’ is acceptable when saying phone numbers, hotel room numbers, post codes or credit card numbers. Zero or nought should be used in mathematical or scientific contexts. I will included the excerpt in the Transum Podcast for this month as it is certainly something all Maths teachers should know.

So here’s the answer to the puzzle as told by William Poundstone in his book “Are you smart enough to work at Google”.

Firstly there is one method involving tossing the coin a large number of times to work out the value of the bias but the best answer comes from Google: “If you toss the coin twice. There are four possible outcomes: HH, HT, TH, and TT. Since the coin favours one side, the chance of HH will not equal the chance of TT. But HT and TH must be equally probable, no matter what the bias. So toss twice, after agreeing that HT means one team gets the advantage and TH means the other does. Should it come up HH or TT, ignore it and toss another two times. Repeat as necessary until you get HT or TH.”

That’s all for now.

ps. Why is a dog with a bad foot like adding 6 and 7? A. Because he puts down three and carries the one.