karthickgururaj

Let's see if there are any other thoughts

Bob doesn't get $100..

One more guessing game! Alice, Bob and Charlie go to a fair. They go to a stall where there is a machine that displays numbers from 1 to 9 at random, one after other, for the sole reason that this puzzle can be framed and posted to brainden. It is not known whether the random process that selects a number in the machine is based on uniform distribution or not.. could be anything.. But it is known that the machine is memory-less, the current number being displayed doesn't influence the next number in anyway. All three stand and watch the numbers for a while. Suddenly Alice turns and tells Bob - "If you can guess the next number within an error margin, I'll give you $100. I won't tell you what the error margin is, but it is not zero". Charlie also offers a similar bet - "If you can guess exactly what the next number is, I'll give you $100. In other words, the bet is same as what Alice is offering, but the error margin in my case is zero". Bob can make two different guesses (if he wants to), one for Alice and other for Charlie. The numbers that they saw before the bet was posed is: { 1, 9, 4, 8, 9, 1, 2, 1, 3, 6, 9, 4, 9, 3, 6, 9, 6} What should Bob do?

Taking off from bonanova's recent post (), a different version of the game is played by Paula and Victor. Paula first selects S, an arbitrary positive integer (> 0). S can be as small or as large as Paula wants it to be. Paula doesn't reveal S to Victor. Paula then selects n integers randomly, (a1, a2, ..., an) (n > 0), with a uniform probability distribution on the interval [1, S]. She tells these numbers to Victor. Then she selects two more integers x and y, again randomly with uniform probability distribution in the same interval. Victor has to decide whether he wants to know the value of x or y. After Victor has made his choice and told Paula, Paula first asks Victor - "A. Guess whether the number I'm going to tell you now is less than S/2 or more than S/2". After Victor answers, Paula doesn't reveal whether he is right or wrong. She instead tells the value of the number. Next she asks, "B. Guess whether the other number is smaller or larger when compared to the one I revealed". After Victor answers, Paula reveals the value of the second number and S (so Victor knows whether his guesses were right or not). Puzzle: What would be Victor's strategy for both the guesses? What would be his chance of winning the first guess?

I don't agree with this it somehow feels wrong, but I'm not able to pin-point where the flaw is.. I'll get back in sometime.. And I'm going to post an other puzzle inspired by this one

(a small correction above) I'll post the full solution in couple of days if no one else responds.

@nuurhasan: Not sure how to react to what said The question is to find the probability that a heads will turn up, but you have assigned a number (1) for heads and 0 for tails. For a fair coin, the probability is 0.5. @k-man: your guess for p is right, but not the response to (b), see bonanova's response.

You are given a coin that has a probability p for heads turning up (and (1-p) that tails will turn up). p is unknown and can be any real number in [0, 1] - all with equal likelihood. You toss the coin 10 times, and 5 times heads turn up. a. (easy) What is your best guess for p (and why)? b. (tricky) What is the probability that p has the value equal to your best guess? c. What is the probability that p = 0.5 (+/- 0.05) ?

I thought so too... but it is not true.

Just brute force. Ah, ok. Then it may be of some value for me to continue with my approach to closure, if only to check whether I get the same results.. Matches with witzar's post..

I saw witzar has already posted a solution which looks complete, so I didn't workout the last step.. @witzar: what was your approach? Something similar?

Without solving the problem, we could also do the following..

Yes, that is right! BTW, this happens to be a good game to play with a 6 year old kid.

I read up a bit about Graham's number - but can you explain the connection to the puzzle here?

I saw this puzzle a while ago.. not sure where. Not too difficult to solve, so give it a go! There are 50 coins of various denominations kept in a single line. Two players (A and B) take alternate turns in removing one coin at a time and adding it to their purse. At any point in time, they are allowed to remove only the coin from the extremities (i,e, either the extreme right coin or the extreme left). Coins in between the line can't be removed. At the end of the game, each player will have 25 coins. Whoever has more net value of coins is the winner. Is this a fair game? If not, who has an advantage? What is their strategy?

Oops, yes!! Sorry. It is XNOR. I don't know what I was thinking.

It is indeed straightforward, so let me start with..

A very interesting puzzle, however. 5 stars

I'm not sure where exactly we are differing, but I think it is still XOR.

A slightly different approach than 'Perhaps check it again'..

I read up the link to the earlier thread posted by bonanova. Now I'm feeling But I doubt if I could have stumbled on the key point.. I really must work with paper (with diagrams of cake cutting), instead of typing out responses. gavinksong had mentioned "it is flipped, not inverted", now I really understand that part. @plasmid: if you do not want to give up, try cutting a real cake Or at the least, draw some realistic 3D diagrams of the cutting and flipping process.

Hey DejMar! This is incorrect. The truth-table does coincide with an XOR operation, but the compound statement is not formulated as an XOR, but as AND. The boolean result is different for the operands if Q is false and X is left-handed, he/she should raise left hand ([0 0] => 0). If person in chair 1 responds to Q1 by raising his right hand, he is person A, and he is (right-handed or not). OR he is person (B or C) and he is left-handed. If person in chair 2 responds to Q1R Q2 by raising his right hand, he is person B, and he is (right-handed or not) OR he is person (A or C), and he is left-handed. Etc. koren was partly correct in recognizing that the questions do not necessarily identify who the person is. karthickgururaj was on the correct track in recognizing that the solution may rely on self-referential questions. Maybe I didn't explain well.. but it is still an xor operation. Hope that helps..

Finite. Ok, I give up

Not sure if I understand the conditions of the puzzle well.. Each prisoner knows their own scheduled time of execution right?