I’m doing a local fun adventure-type race with my daughter on Father’s day, and if I answer the following puzzlers correctly we get a time bonus (I think). It’s no big deal, we’re just doing it for fun, but this will give you guys a chance to show how smart you are! I think I know the answers to questions 2 and 3, but tell me what you guys think:
**Question 1. You want to travel 100 miles on a Big Wheel and you have 2 spare tires. You must use all 5 tires equally and have equal mileage on each of the 5 tires at the end of the trip. You can only use 3 tires at a time, so you’ll have to change tires during the trip. At the end of your trip, how many miles will each tire have been used? (For the purpose of this question - all tires/wheels are the same size) ** ****
**Question ****2. You have twelve 12-packs of bottled green tea. All the bottles contain 12 oz’s of tea except for one of the 12-packs, which has only 11 oz’s in each bottle. You’re given a scale with low batteries and it can only take 1 measurement. How do you determine which 12-pack is short? ****(You can’t determine the answer by looking at the bottles and you must use the scale to find the answer. You can separate the bottles in the 12-packs, but can’t open the bottles. Assume that the weight of the glass bottle is zero). ** ****
take 1 in the first, 2 in the second,…,12 in the last one.
so you have 78 bottles. if all were 12oz, the weight would be 78x12.
if the first pack is lighter the weight will be 78x12 - 1
if in the second 78x12 - 2
etc.
If you put split up each 12 pack into a group of 7 and 5, then you could make up 6 12 packs containing 3 12packs of 5 and 3 12 packs of 7. So now you have 2 groups of 6 12packs. Put these 2 groups on the scale… the lighter side is the side with the 2 extra bottles that weigh less…
…done !!
{EDIT}…crap… I thought it was a balancing type of scale… not a digital scale… crap… I thought my answer rocked !!
Wow (and I mean that sincerely). Maybe my guidance counsellor was right. Learning math does give you the tools to solve all problems.
Does this only work if you assume 12 ounces is a measure of weight rather than volume?
Looking at a bottle of 12 oz. of green tea, I would think this meant twelve “fluid” ounces in volume rather than the “avoirdupois” ounce for weight measurement. Since 12 fluid ounces of green tea would be a bit more than 12 ounces in weight (something like 12.5 based on the water equivalent), would you need to know this exact weight first in order to solve your equation?
actually it works for weight not necessarly for volume…because then the liquids in each bottle may be different hence a different weight, and no possible conclusion could be drawn
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yes but then several combinations of bottles and different densities could mess up your results as several linear combinations could yield the same result. So you wouldn’t be able to answer.
