In honor of the holidays, I thought I'd post this question, which I frequently have posted elsewhere over the years. Here goes: As we all know, New Years day and Christmas day are exactly 1 week apart. That said, in 1917, that was not true. Why not?
Because in 1917 New Years Day was at the start of the year and Christmas all the way at the end, many months later.
That's correct! That's actually the fastest I've ever seen someone come up with the correct answer. Usually, people come up with all sorts of historical mumbo jumbo to explain it.
The next one is not holiday related, but I may as well post it as well. I'll post another if you guys solve it. There is a circular race track that is exactly 1 mile in circumference. If you drive halfway around the track at 30 mph, how fast would you have to travel the rest of the way in order to have an average speed of 60 mph for the entire trip?
Wait, you'd have to keep going 30 mph because that's a half-mile/minute, and you'd go around the whole track in a minute, which is 60 mph.
It's impossible. Let X be the speed which is required of the second half-mile. Time = distance/speed. 0.5/30 + 0.5/X hours would be the total time required. With an average speed of 60 MPH to travel 1 mile, the time required would be 1/60 hours. Hence, 0.5/30 + 0.5/X = 1/60. Cross-multiplying, 0.5X + 15 = 0.5X. We would end up with 15 = 0, which is obviously not true. Hence, there is no speed that will give an average speed of 60. If you somehow manage to do this in real life, a Nobel prize in physics should be in short order.
Correct! There's actually a much easier way to explain it: The total distance is 1 mile -- in order to average 60 mph, you have to drive the entire circumference in 1 minute. At 30 mph, it takes a minute to drive 1/2 mile, which is the distance that was already driven. Hence, you've already driven for 1 minute, and have 0 minutes left to complete the circuit in order to average 60 mph. Congratulations!
This might be the toughest one (or the easiest one) depending on how your brain works. There's an old riddle -- some of you may know it, but the traditional answer to it is not the most interesting part of the riddle. The original riddle goes as follows: A man travels 10 miles south, shoots a bear, then travels 10 miles east, and 10 miles north and winds up back where he started. What color was the bear? The traditional answer to that riddle is "white" because, as the person telling the riddle explains, the only place where you can travel 10 miles south, 10 miles east, and then 10 miles north, and wind up back at where you started is at the north pole. Clever riddle. Unfortunately the explanation of it turns out to be wrong. My question is, where else on earth, BESIDES THE NORTH POLE can you travel 10 miles south, 10 miles east, and then 10 miles north, and wind up back where you started? Note that I do not require an EXACT answer -- just a good enough description/explanation.
10 + 5/PI miles north of the south pole. You travel 10 miles south. Then traveling 10 miles east gets you in a perfect circle. Then 10 miles north puts you back where you started. The simpler answer is 10 miles north of the south pole but that has problems with how you go 10 miles east and which way is north.
Correct! That's the simplest answer (you didn't need to give me the 5/pi -- my math is rusty nowadays but I'll take your word for that. All I needed was the part about circling the pole. I won't bother with the follow-up question -- you can also be a little closer than that and do N circuits around the pole where N is any integer (there's an infinite number of locations, in other words).
I have one final brain teaser that should be a lot easier than the others: Spell one word out of the letters in "NEW DOOR".
