jasen

@bonanova, thanks for correcting me.

I can prove this hipothesis is wrong !

bonanova, this your puzzle drives me mad

How about this :

Someone still can argue that your reasoning is not a prove.

I think this strategy is better

I think I can write every rational number in repeating decimals 1 = 0.99999999........ 4 = 3.99999999....... 17.5 = 17.4999999.... and so on. wheather my statement is right or wrong, prove your agreement or objection.

what you mean "they can open at most 50 boxes" ? total boxes they can open or each prisoner can open 50 boxes If each prisoner can open 50 boxes, I think, surviving probability is more than 50%

I have create a program to count braces from 1 to 5000

I was quoting bonanova solution/answer, not my proposed strategy. Your strategy is not applicable, you can't bet more money than you have, if your current money is 50$, your original money is 100$, so 2*100-50 = 150$, which you don't have. Now I explain, my proposed strategy.

I have run computer simulation with your strategy, and your chance to win is 50%

Consider this : Keep bet half of your money, and your probability to win is 100% theoritically this is true. do you agree this strategy ?

very close! just wrong 1 digit. the question is asking for sum bellow 1000.

good start but wrong, your way to find out sum of multiple 3 and 5 are still wrong.

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000. It is easy to find the answer using computer, but it's more interesting if we can solve it without coding.

The game is guessing head or tail of a coin toss, so the probability to win is 50%

In a gambling game, the rules are : you bring an amount of money, you can bet any amount of money you like, the game stop if : 1. your money have doubled (exactly 2x your first amount of money) 2. or you lose all of your money. you can't stop in the middle of the game. example : if you bring 10 dollars: 1. If you bet all your money in the first bet, so if you win you get 20 dollars and game over, or if you lose, you lose all your money and game over. 2 If you have already win 19 dollars, so in the next game you maximum bet is only 1 dollar. what is your strategy to win the game ?

Right ! This case is one of the famous misleading sequence

wrong! You are trapped. Check again.

Place 6 points along a unit circle, in such a way that when you draw all lines connecting every pair of points, no more than two lines pass through any interior point. How many regions does this divide the unit disk into?

modified Stern-Brocot Tree to third sequence. 3rd sequence 34/55 157/254 123/199 212/343 89/144 233/377 144/233 199/322 55/89 since it use fibbonaci number, which is relatively prime, so the fraction is already in simple form. so there is no fraction with 55<b<89

maybe this have something to do with math golden ratio, which it close to 1.6180339887...