BrainDen.com - Brain Teasers # k-man

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1. k-man's post in Bus Schedule was marked as the answer
Highlight text below to see my theory
While the average wait time should be 15 minutes, there are longer and shorter wait times during the day. A random placement of a point in time is more likely to land on a longer wait time period. For example, if we look at a 1 hour period that has two 10-minute waiting intervals and two 20-minute waiting intervals, then an average wait time is 15 minutes, but a random point in time selected within that hour is twice more likely to be within the 20-minute interval.

2. k-man's post in The early Commuter was marked as the answer
3. k-man's post in shooting game was marked as the answer
4. k-man's post in Combinations Problem was marked as the answer
My attempt...

5. k-man's post in How big is the ladder was marked as the answer
Since no one has attempted to answer this yet...
Given that John and Julie play on the same level and have 50/50 chance of winning any particular game, I agree with Bonanova that Julie has 50% chance of winning whatever series they choose to play. However, I think the OP is asking about the probability of Julie winning with the score 4:3 in the 7 game series vs. the probability of winning 5:4 in the 9 game series. Those probabilities are different...
7. k-man's post in Half-balls was marked as the answer
Assuming that all heavy halves are identical (and therefore all light halves are identical too), so we can pair any heavy half with any light half to create a sphere.
8. k-man's post in Cylinders was marked as the answer
Looks like after the site update I can now upload Excel files, so here you go...
Drum Decorator.xls
9. k-man's post in Half as old as my brother was marked as the answer
10. k-man's post in Cosmetic Surgery and the Worm was marked as the answer
Looks like you're right, BMAD. I haven't taken my 9-long worm example far enough to see that the adversary cannot continue to maintain that pattern indefinitely as long as surgeon does the right thing.

11. k-man's post in Changing times was marked as the answer
Considering that there is a \$1 coin, the maximum is limited only by the availability of the \$1 coins. Without using \$1 coins, I don't see how you can have more than 99.
12. k-man's post in Equilateral Triangle: Color and distance II was marked as the answer
Ignore my previous post. I got my numbers mixed up.

13. k-man's post in Airplane with or without wind was marked as the answer
I think your simplified analysis still doesn't address the cross wind correctly. Let's say that the closed path is from point A to point B and back in a straight line. It will take longer with the constant cross wind than without any wind.

14. k-man's post in get Bent was marked as the answer
15. k-man's post in Make 15 was marked as the answer
16. k-man's post in Cutting a rectangle was marked as the answer
Assuming you meant a rectangular solid...

17. k-man's post in Hexagon: Diagonals and sides (If and only if?) was marked as the answer
18. k-man's post in "Big" Triangles was marked as the answer
Not sure if this qualifies for c), but should be sufficient for a) and b)

19. k-man's post in k-man's kasino was marked as the answer
Hah! Who would know that better than k-man?

20. k-man's post in Black and white square table was marked as the answer
For any nxm. I don't have a rigorous proof, but I think it would go along these lines...

21. k-man's post in Polygons make a line was marked as the answer
Using the interpretation of "crossing" as "having a common point with"...

22. k-man's post in Sides = Diagonal was marked as the answer
23. k-man's post in Tiddlywinks tournament was marked as the answer
24. k-man's post in Conditionally conflicting was marked as the answer
25. k-man's post in Pour over this was marked as the answer
Oops, you're right. I skipped a pour.

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