[quote]Bujo wrote:
Scientific studies have shown that there is a direct, positive correlation between foot size and performance in spelling bees / spelling tests. How can you explain this correlation?
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This one might not be as simple as I think it is, but: your foot size increases as you get older. You also learn how to spell more words as you get older. At some point (say, age 25 or so) there would no longer be a correlation, but the strength of the correlation from ages 3-25 would be strong enough to carry the study.
[quote]Hambone1818 wrote:
There are two lengths of rope. Each one can burn in exactly one hour. They are not necessarily of the same length or width as each other. They also are not of uniform width (may be wider in middle than on the end), thus burning half of the rope is not necessarily 1/2 hour.
By burning the ropes, how do you measure exactly 45 minutes worth of time?
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Start by burning one rope from both ends and the other rope from just one end. As soon as the first rope has completely burnt, start burning the second rope from the other end so that it is now burning from both ends. A half hour has now passed, when the second rope has completely burnt, 45 minutes will have passed.
Three men go to a motel and pay the owner $10 each. Later the owner realizes he has overcharged them and sends the bellhop to refund them $5. The bellhop decides $5 is too difficult to split 3 ways, so he pockets $2 and gives each of the three men $1 back. Thus each man paid $9. We know that the men originally payed $30, but they ended up only paying $9 each, plus $2 to the bellhop. 9+9+9+2=$29. Where did the extra dollar go?
The last one is a bit misleading. It’s easier to see if you just track the total money.
Entering the hotel:
Man #1 = $10
Man #2 = $10
Man #3 = $10
Bellhop = $0
Hotel = $0
after the refund to the customers:
Man #1 = $1
Man #2 = $1
Man #3 = $1
Bellhop = $2
Hotel = $25
The part that trips you up is the “9 dollars each plus $2 to the bellhop.” In reality, each man pays 9 dollars total, 25/3 of a dollar to the hotel and 2/3 of a dollar to the bellhop. The question is phrased so that it appears as though the men paid more than $9 each.
[quote]tedro wrote:
Three men go to a motel and pay the owner $10 each. Later the owner realizes he has overcharged them and sends the bellhop to refund them $5. The bellhop decides $5 is too difficult to split 3 ways, so he pockets $2 and gives each of the three men $1 back. Thus each man paid $9. We know that the men originally payed $30, but they ended up only paying $9 each, plus $2 to the bellhop. 9+9+9+2=$29. Where did the extra dollar go?[/quote]
Their cost was $27 = 25 + 2. The three extra dollars were returned to them. The 2 dollars is included in the 9 + 9 + 9.
[quote]Bujo wrote:
Scientific studies have shown that there is a direct, positive correlation between foot size and performance in spelling bees / spelling tests. How can you explain this correlation?