BrainDen.com - Brain Teasers

# k-man

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13

1. ## Bus Schedule

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.

3. ## Symmetrical equation

...or more in general...

5. ## 7 brothers

New York. And they all work as cab drivers.

7. ## Random bullets

I built the probability tree using PowerPoint. It's not freeware, but it's easy to learn and use. If you don't have PowerPoint you can try Google Docs, but I don't know if they have the same widgets that PowerPoint has or not.
8. ## Random bullets

I've been following this thread without comment as there wasn't anything I could contribute (didn't have the aha! moment like harey did). I'm convinced that harey's approach is correct. Probably the easiest way to see it is to draw the probability tree of complementary events (see below). The green track leads to the complete annihilation with total probability established earlier, the red track is the "no collision" track with total probability of 1/n! and the yellow tracks are all the partial annihilation tracks. This tree also explains jasen's finding that the most likely outcome is that 2 bullets remain. Half the leaf nodes of this tree will have that outcome and the total probability will be the sum of those leaf node's probabilities.

cheating...
10. ## Farming

My thoughts...
11. ## IQ test question

I would agree with jasen's answer. I think you're reading too much into details that are merely artifacts of the quality of the test. In this second puzzle there are 9 ways to combine 2 sticks of 3 types. 8 of them are given and the 9th is missing.
12. ## IQ test question

Well, I don't have the context that you have as I don't see the rest of the questions, but looking at this question alone I wouldn't call it particularly complex and my solution/answer seems reasonable to me. BTW, I've never seen a test where two of the possible answers were exactly the same as in this test.

15. ## Combinations Problem

My attempt...
16. ## How big is the ladder

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...
18. ## Half-balls

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.
19. ## Image puzzles

The first image No idea what the other 2 images mean.
20. ## Cylinders

Looks like after the site update I can now upload Excel files, so here you go... Drum Decorator.xls
21. ## Cylinders

Welcome back, araver!

24. ## Cosmetic Surgery and the Worm

It seems that I disagree as there should always be a way for the surgeon to win. 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.