BrainDen.com - Brain Teasers # Prime

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1. Prime's post in Ultimate Mate was marked as the answer
Found the ultimate mate in 9 moves.

2. Prime's post in Let's meet up was marked as the answer
3. Prime's post in Simple money probability was marked as the answer
Not only I forgot about half dollar coin in my previous post, I also made few arithmetic errors in calculating probabilities.
Although, the answer who has a better probability is the same.

4. Prime's post in A shady game?! was marked as the answer
The code calculates the exact probability for the average payoff with the best strategy (unless I messed up.)
Both simulation and code must take into account the cards leaving the deck. Also, must discard invalid (in terms of strategy) variations. E.g., a draw like (13, 13, 8).
The criteria for the staying card on the third turn can be established analytically (see the spoiler.)

5. Prime's post in How many arms do you have? was marked as the answer
6. Prime's post in Is this conjecture regarding primes true? was marked as the answer
7. Prime's post in My friend and I play in a chess tournament was marked as the answer
8. Prime's post in Blue eyes and green eyes was marked as the answer
I suppose, blue eyed child also must play part in figuring out question 1. I only took it into account for figuring out question two, so my previous answer is wrong.

9. Prime's post in Sharing Circles was marked as the answer
This way it's more interesting. I understand, one person has 4 times the money of his neighbor at the end of the game.

10. Prime's post in Getting paid for good grades was marked as the answer
11. Prime's post in three card puzzle was marked as the answer
12. Prime's post in Perfect number was marked as the answer
I am only aware of this general rule.

That is not to say there aren't any other possibilities for finding perfect numbers.
13. Prime's post in square vs circle was marked as the answer
14. Prime's post in For Bushindo - (others try at your own risk) was marked as the answer
I am uncertain, what uncertain means in this context.
Cole's first shot strategy is clear. He must shoot himself in the foot thus exiting the duel with a non-fatal injury. (Hopefully, he does not miss.)

15. Prime's post in Colorful cubes was marked as the answer
Actually, we should split the difference and go with 27.

16. Prime's post in Lucky Tickets was marked as the answer
Going with the following assumptions as answers to my questions:
2. We work with the sum of numbers, not digits.
3. The school No. 7 is in Moscow in the vicinity of MSU (МГУ) and Vernadski Prospect.

I have a different proof of the same, which gives even more insight into divisibility rules, but it would take longer to explain.
We have another Divisibility puzzle going here: http://brainden.com/forum/index.php/topic/15583-more-divisibility/?p=328196]More divisibility
17. Prime's post in Stopping and Turning back hands of time was marked as the answer
I see, I mixed up the adavance of the hour hand with the elapsed time for each cycle. And I calculated period incorrectly for the second part in my previous post.
Still, after the corrections, I get a different answer. My hour and minute hands will meet a lot sooner.

Why rejecting the occurences where the clock hands meet at 12 in a mid-cycle?
I see nothing in the OP prohibiting that. In fact, the clock hands will meet again at 12 on a mid-cycle before they do so after a whole number of cycles.

18. Prime's post in An "Oldie" with a twist of lemon was marked as the answer
Nice problem.
19. Prime's post in The birthday coincidence was marked as the answer
Time's up.

20. Prime's post in Stamps and foreheads was marked as the answer
I’ll try again.

21. Prime's post in The Hobbled Rook Tour was marked as the answer
Same as Kingly Tour.

22. Prime's post in Closed form expression on steroids was marked as the answer
But they don't need to be integers, those 11 periodic values.

23. Prime's post in Six integer equations, Eight digits was marked as the answer
I found couple solutions, but not with as many digits, I'm afraid.

24. Prime's post in Ultimate Mate was marked as the answer
Found the ultimate mate in 9 moves.

25. Prime's post in Hitting 137 was marked as the answer
It seems to stand the reason...

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