Math Is Fun Forum

draken_kiele

Member

Registered: 2022-08-17

Posts: 1

Magnetic Symbols Problem

I'm a computer science teacher.  I offered this problem to my students for extra credit.

If you have a magic bag containing and infinite amount of magnetic letters, numbers and symbols as ("A-Z", "0-9", with "+", "-", "/" & "=") in six colors (red, orange, yellow, green, blue and purple) and you want to pull one item out of the bag each second until you have one of each letter, number and symbol in each of the six colors, how long will it take to complete your set?

Note:
There are 40 different shapes, each in 6 different colors, in the bag.
There is no multiply sign because you can use either the "X" or the "+".

Explain your answer.

Median Joe

Member

Registered: 2019-12-04

Posts: 8

Re: Magnetic Symbols Problem

I think this is an example of the coupon collector's problem (see https://en.wikipedia.org/wiki/Coupon_collector%27s_problem).

The formula for the expectation (average number of draws until you have the whole set) is n x (1/1 + 1/2 + 1/3 + ... + 1/n), and in this case n = 6 x 40 = 240 "coupons". Therefore at the rate of 1 draw/second it will take 240 x (1/1 + 1/2 + 1/3 + ... + 1/240) = 1455 seconds, or 24 mins 15 seconds.

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