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?
Reference: This question comes from the book “Are you smart enough to work at Google”.
How did you use this starter? Can you suggest
how teachers could present or develop this resource? Do you have any comments? It is always useful to receive
feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
Click here to enter your comments.
If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:
This starter has scored a mean of 2.0 out of 5 based on 1 votes.
This question comes from 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.
The answer to the puzzle as told by William Poundstone, the author of the book.
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.”
How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world. Click here to enter your comments.
Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon search box and some items chosen and recommended by Transum Mathematics to get you started.
Texas Instruments Nspire Calculator
This handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TI-Nspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TI-Nspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others.
For the young people in your life it is a great investment. Bought as a gift for a special occasion but useful for many years to come as the young person turns into an A-level candidate then works their way through university. more...
Apple iPad Pro
The analytics show that more and more people are accessing Transum Mathematics via an iPad as it is so portable and responsive. The iPad has so many other uses in addition to solving Transum's puzzles and challenges and it would make an excellent gift for anyone.
The redesigned Retina display is as stunning to look at as it is to touch. It all comes with iOS, the world's most advanced mobile operating system. iPad Pro. Everything you want modern computing to be. more...
Before giving an iPad as a Christmas gift you could add a link to iPad Maths to the home screen.
Click the images above to see all the details of these items and to buy them online.