BrainDen.com - Brain Teasers  # Logophobic

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1. Logophobic's post in Making a spiral was marked as the answer
@bonanova It appears to me that you are way off:

2. Logophobic's post in alphametic with modulo was marked as the answer
3. Logophobic's post in Star Puzzle : Determine which circles are True and which circles are False was marked as the answer
4. Logophobic's post in How many spin-able numbers are there from 0 to 99999 ? was marked as the answer
5. Logophobic's post in 5x5 statement table. was marked as the answer
I wish there were some easier logic than trial-and-error (if there is, I missed it), but I have found the solution:

6. Logophobic's post in Who should do what was marked as the answer
7. Logophobic's post in Rubic cube's face into date was marked as the answer
8. Logophobic's post in Star area was marked as the answer
I believe you are mistaken.

9. Logophobic's post in Arrange the digits from 0 to 9 into a number with inequality constraints was marked as the answer
10. Logophobic's post in Help the police to reveal the hidden password. was marked as the answer
Description:

11. Logophobic's post in Dividing a gathering for friends was marked as the answer
12. Logophobic's post in Light Bugs was marked as the answer
There are multiple solutions:

13. Logophobic's post in 3 x 3 table with constrains (continued) was marked as the answer
The are essentially the same solution.
3 6 4            -3 -6 -4
8 9 2  x  -1  =  -8 -9 -2
1 5 7            -1 -5 -7
-3 -6 -4     10 10 10     7 4 6
-8 -9 -2  +  10 10 10  =  2 1 8
-1 -5 -7     10 10 10     9 5 3
14. Logophobic's post in Find the number was marked as the answer
15. Logophobic's post in 4-axis Rubik's Cubes was marked as the answer
I see, and the best solution is

16. Logophobic's post in Equal sum of numbers was marked as the answer
Simple:
Alternately:
Question:

17. Logophobic's post in Same Ratio was marked as the answer
Except that there is one result (b=c) that you did not test:
18. Logophobic's post in Dangerous safari? was marked as the answer
19. Logophobic's post in star was marked as the answer
20. Logophobic's post in 3 brothers ages was marked as the answer
Hint:
Solution:
21. Logophobic's post in Radar clock was marked as the answer
22. Logophobic's post in Another rabbits problem was marked as the answer
23. Logophobic's post in Rectangram was marked as the answer
24. Logophobic's post in Highest of the lows was marked as the answer
Ah. In that case my simulations agree with yours. I noticed a certain relation between N and EV, so I ran a few more simulations.
The first number is N, the second is EV based on simulation. The third is a very simple calculation. (See below.)
100  88.21  87.50
200 182.96 182.32
300 278.84 278.35
400 375.62 375.00
500 472.53 472.05
600 569.96 569.38
700 667.59 666.93
800 765.54 764.64
900 863.13 862.50
1000 961.13 960.47
If that wasn't evidence enough:
1000 960.85 960.47
2000 1944.74 1944.10
3000 2932.26 2931.53
4000 3921.39 3920.94
5000 4912.13 4911.61
6000 5903.97 5903.18
7000 6896.78 6895.42
8000 7888.41 7888.20
9000 8881.87 8881.41
10000 9875.06 9875.00
The very simple calculation?

25. Logophobic's post in Three-birthday paradox was marked as the answer
Based on simulated trials, the answer is...
I recorded 100 runs of 100,000 with this number. The minimum was 50,046. The maximum was 50,316. The average was 50,177.64. Final result: 50.18%
Then I considered February 29, which was conveniently omitted in those trials. I repeated the process, allowing for leap day in its proper ratio. The minimum was 49,891. The maximum was 50,068. The average was 49,999.04. Final result: 50.00%
Very interesting. Given this number of people, the probability that at least three share a birthday might be ever-so-slightly less than 50%.
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