Enigma 334: Biggabagg’s Bettamix
26 February 2016
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From New Scientist #1482, 14th November 1985 [link]
My two elder sisters love Mr Ivor Fitzclarence Biggabagg’s seductive sweet-counter. His “Bettamix”, a random mixture of liquorice and blackcurrant gums, is splendid value, they reckon: each buys a quantity every week. When they get home, they allow me to pick one gum for myself. Isn’t that nice of them?
I hate liquorice and love blackcurrant, but unfortunately they won’t let me just look and choose a blackcurrant gum. They do however let me first inspect the contents of each bag. Then I can either choose one bag at random and then pick a gum at random from it or mix up the contents of both bags and then pick a gum at random.
You will be glad to hear that I have now worked out a simple rule for deciding which of the two methods gives me the better chance of a blackcurrant gum.
I was surprised last week to find that it didn’t matter which method I chose. Anne’s bag contained 6 liquorice and 14 blackcurrant gums. Pam’s held 18 liquorice and quite a few blackcurrant.
Before I had a chance to choose, Anne removed some of the blackcurrant gums from Pam’s bag and asked me, in this new situation, to decide which method. And again I was surprised to find that it didn’t matter which method I chose.
How many blackcurrants did Anne remove?
Note: A correction was issued to this puzzle in New Scientist #1485 (along with the solution), the puzzle statement above has been modified accordingly.