BrainDen.com - Brain Teasers

# harey

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1. ## Beetle's meeting up

I think it is a pity that the solution is not posted when nobody finds it. So here we go:
2. ## Sixty-one marbles or fewer

I do not accept. .
3. ## Sensors

Prayer to bona alma: - correct the post 4 with the correction from the post 5 - delete in the post 4 remarks that are not necessary anymore - delete the post 5 - delete this post ...and pray with me that bmad concedes it is the Best Answer

5. ## Sensors

Correction: B sends: - if(measurement<4) measurement else 7-measurement. P.S. It would not be bad if the table in my previous post magically appeared in a fixed font.
6. ## Sensors

Sorry I cannot hide it. Maybe because of the font? Edit: Definitely, I have a problem with the editor.
7. ## game theory ...tough

Reasoning from a similar problem:
8. ## Having sisters

@Grimbal You can continue: - there are 50.5 boys born per 49.5 girls. - women live longer.
9. ## 401 unit diameter Circles in a 400 unit rectangle

Really easy!!! And even more. No one said that the 401 circles may not have a smaller diameter. No one said that they may not ovelap.

12. ## Numbered Foreheads Concluded

We know that A sees B=334 and c=334 - A CANNOT see B=335 and C=334. (Not to confound with: "As this information in not available to him, he ASSUMES he has 334 or 335.") So my first answer was correct. In the 2nd try, I got lost and could not correct quickly enough.

15. ## Numbered Foreheads Concluded

I know a better and harder version, if I find it, I'll post it. Does it matter if it is in French?
16. ## Having sisters

Myself, I would prove it for N=0 and leave the proof for N>0 to the reader If you try for some N, you quickly see the law.
17. ## Having sisters

@bmad: I do not think my answer was the best one - after all, the chances were 50-50 phaze answered much better, he explained WHY.

19. ## Guess 1 out of 100 numbers

I like the Phil1882 idea of modulo and tried the following rule: It works for some examples for N=4 (with no counterexample so far). The next steps should be an exhaustive computer simulation and a strong therie. Someone is willing to continue?
20. ## Grazing cows

The first part did not require much calculation . As usually, I made an arithmetic error. I tried with b=60, c=80 - plasmid is correct.
21. ## Let's meet up

They can follow other than mirror paths to meet at the same point. If they meet, they meet at the diagonal. The probability (for each one) to get to a particular point on the diagonal is: Pascal's triangle/(2 power n). I hope someone finds a formula for the product.

24. ## Ghost Ships

If I posted this problem, I would ask to clarify: 1) why the lines H and I cannot be parallel; 2) crossing trajectories do not necessarily imply that the ships collide. BTW, the sea should be endless (so that H does not reach her destination before colliding).
25. ## Fuel consumption

You got the first part to 97% - I wanted to hear "section of a pipeline along the trajectory". The tank of the U.S. scenario corresponds quite well to the pipeline, just the section of a tank is not measured in 1/m2, so the second part of the problem is still open.
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