tag:blogger.com,1999:blog-3722233.post116371565218870162..comments2020-09-30T09:13:54.199-05:00Comments on Computational Complexity: Pepsi MathLance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-3722233.post-1163889920711677972006-11-18T16:45:00.000-06:002006-11-18T16:45:00.000-06:00I think you didn't calculate it right.Actually, I ...I think you didn't calculate it right.<BR/>Actually, I think that, in average, you pay the price of six bottles while getting seven bottles which means a discount of 1/7 or less than 15 percent.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-1163873278789507032006-11-18T12:07:00.000-06:002006-11-18T12:07:00.000-06:00On the other hand, putting "buy 10 get 1 free" is ...On the other hand, putting "buy 10 get 1 free" is not the same as "get 1 free", because with high probability it will leave you with unused discount caps when the promotion is over. Much like pyramid games...Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-1163825604997689292006-11-17T22:53:00.000-06:002006-11-17T22:53:00.000-06:00One the other hand, if you sum the series, you get...<I>One the other hand, if you sum the series, you get:<BR/>1) Get 6 sodas - get 1 winning cap<BR/>2) Get 2 sodas (one free) - get 1/3 winning cap<BR/>3) Get 2/3 sodas (1/3 free) - get 1/9 winning cap<BR/>...<BR/>The sum is you get 1 1/4 sodas free out of 8 1/2. That's 5/34. <BR/></I><BR/><BR/>That's just bad arithmetic. Notice that the total # of sodas is<BR/>6(1+1/3+1/9+...) whereas the number of free sodas is (1+1/3+1/9+...). Hmm. I wonder what that ratio is?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-1163802825638817042006-11-17T16:33:00.000-06:002006-11-17T16:33:00.000-06:00One the other hand, if you sum the series, you get...One the other hand, if you sum the series, you get:<BR/><BR/>1) Get 6 sodas - get 1 winning cap<BR/>2) Get 2 sodas (one free) - get 1/3 winning cap<BR/>3) Get 2/3 sodas (1/3 free) - get 1/9 winning cap<BR/>...<BR/><BR/>The sum is you get 1 1/4 sodas free out of 8 1/2. That's 5/34.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-1163782202926095602006-11-17T10:50:00.000-06:002006-11-17T10:50:00.000-06:00A simple argument:Suppose you have a total of n bo...A simple argument:<BR/><BR/>Suppose you have a total of n bottles, where n is large. Then 1/6 of them have winning caps, which means 1/6 of the bottles were given for free.<BR/><BR/>NoamAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-1163750563485099012006-11-17T02:02:00.000-06:002006-11-17T02:02:00.000-06:00Lance your first argument 16.7 percent discount is...Lance your first argument 16.7 percent discount is right.<BR/><BR/>Another arguments is that 6 caps are spent to get 1 drink and 1 cap.<BR/><BR/>Therefore a cap is worth 0.2 drinks.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-1163724112509908372006-11-16T18:41:00.000-06:002006-11-16T18:41:00.000-06:00Here in New York, I don't know of any merchant tha...Here in New York, I don't know of any merchant that actually honors these discounts. So you end up with a 0% discount.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-1163723659661942202006-11-16T18:34:00.000-06:002006-11-16T18:34:00.000-06:00The implication is that "buy n, get 1 free" is an ...The implication is that "buy n, get 1 free" is an equivalent discount for all n, but it seems to break down for large n. (n>6, in this case?).<BR/><BR/>Call me risk averse if you like, but I'd like to go the merchant and say "I waive my rights to any free sodas, now please sell me soda at a 10% discount, and you'll be better off in the long run". Somehow, I don't think they would buy it. <BR/><BR/>GrahamAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-1163723333127717772006-11-16T18:28:00.000-06:002006-11-16T18:28:00.000-06:00"50% off next purchase"It doesn't seem equivalent ...<I>"50% off next purchase"</I><BR/><BR/>It doesn't seem equivalent to me. 100% off next purchase seems equivalent...Anonymousnoreply@blogger.com