Brain Teasers
Soda Bottles
Sally likes soda very much. At the local convenience store, for 5 empty soda bottles she receives a full bottle. As part of the Girl Guide's recycling initiative, she manages to collect 77 empty bottles. How many bottles of soda will she be able to drink in total?
Answer
19 bottlesFrom the initial 77 bottles, she receives 15 full bottles (with 2 spare empties). From the 17 empties, she receives 3 more full bottles (with 2 spare empties). From the 5 empties she receives one final full bottle.
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Comments
'scuze me That was fun! Thanks!
I think the answer is not 19, but 96. She was able to drink the initial 77 bottles, too!
She didn't drink the first 77. She got them from the recycling drive.
This was a good one; thanks, I enjoyed it. After getting the answer, I wondered if one could derive a general formula for S, the number of sodas you can earn, as a function of N, the number of empty bottles you start with. (stop reading here if you want to do this one yourself. Have you stopped reading? OK, spoiler coming. I mean it. Stop now). The answer is S = INT((N-1)/4) where INT is the integer portion of the fraction. This is because you have a geometric series of sorts with ratio 1/5 (N + N/5 + N/5^2 etc.); we all remember that the formula for the sum of a geometric series is A/(1-r) where A is the first term and r is the ratio. However, because of the remainder stuff it is more complicated than that. Anyway, I am pretty sure that's a general formula, but I am not sure I can prove it. I did come up with an induction proof (by induction on N)but I'm not sure it's valid. My brain is rusty!
um. it was very... mathlike.
Tricky... like it
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