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Problems that Caught my Eye

June 11, 2012

I was searching for equable shapes and came across these two problems that I like the look of on the MEI website

http://www.mei.org.uk/index.php?page=

I’ve spent much time looking at them yet but I thought I’d share them anyway:

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Finding the highest card

On 30 cards I write 30 different numbers, shuffle them thoroughly and place them face down in a pile on a table. You have no idea how big any of my numbers are. You turn over one card at a time, look at the number and decide whether you want to stick with that card or discard it and turn over the next card. Once a card has been discarded you cannot go back to it. What strategy should you use in order to maximise your chances of selecting the card containing the biggest number?

A possible strategy: Do not keep any of the first 10 cards you turn over but remember the biggest number and call this number N. From the 11th card on, as soon as you see a number bigger than N, stop there. Of course, you might not see another number bigger than N in which case you will end up turning over all the cards without ‘winning’.

With this strategy, what is the probability that you will select the biggest number?

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One Comment
  1. Fawn Nguyen permalink

    Thanks, Dave, for the link to MEI. I love these puzzles. I don’t love that it’s almost midnight, and my head is now stuck on the problems! 🙂

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