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Yet-another-coupon-collector's-problem:
I know this may be a very similar question to others, but I couldn't crack it and this one has a 'special knack' to it, please bear with me:

  1. 260 specific coupons are in the pool (will give you completely random coupons every time, not taking into account what it gave out already)
  2. you pull 20 (random, but all different) coupons out per try (this is the 'special knack')
  3. how many times do you have to pull until you pulled 100% of the coupons
  4. (follow-up: how many times do you have to pull until you pulled ~95% )


(Complete flabbergastedness:

  • How to input this problem in wolframalpha?
  • How to calculate this using the browser console (vanilla javascript))


thanks, any help a lot appreciated

user2305193
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  • When you pull your $20$ random coupons out, is that with replacement? Also, if you don't have to put the coupons back, you can get them all in just $13$ tries, so that's what I'd recommend. – Shagnik Jul 29 '16 at 08:45
  • replacement I guess means you get completely new coupons, from an unlimited pool. Then yes, that is the case, thanks, edited – user2305193 Jul 29 '16 at 08:46
  • So there are 260 specific coupons to collect and you have an unlimited supply of boxes right ? And the $20$ coupon in one box are chosen randomly, with possible replacement ? – Zubzub Jul 29 '16 at 08:47
  • Sorry, I shouldn't have joked and obscured the real question. On a single try, when you choose $20$ coupons, are they all distinct coupons, or could you choose the same coupon several times? – Shagnik Jul 29 '16 at 08:48
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    Thanks guys, I made it more specific according to your suggestions, sorry for the unclear question – user2305193 Jul 29 '16 at 08:49
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    Downvote: Is this question too simplistic - in which case I don't get why someone just doesn't post the formula - or just still too unclear? This is not homework, and I did my research, went on Wikipedia/searched math.stackexchange.com, I just can't crack it and would appreciate help? At least some link to a good resource? – user2305193 Jul 29 '16 at 16:18

1 Answers1

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I found this Formula for approximating this problem, I hope you guys agree:

$$\frac{log(1−x/260)}{log(1−20/260)}$$

(where t batches of size b drawn from n different coupons)

That would yield the following results: for 247 (95%) different coupons: 37.45 times

Community
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user2305193
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