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DanielFishman
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OK. If you're in the UK, you've probably seen this already (sinc Derren Brown did it on TV quite recently), but hopefully most people won't have.

Two people play a game. The first player picks a string of three heads or tails (ie HTH or TTT, for example); then the second player does likewise (he can't choose the same one, though).
Then you toss a coin repeatedly until one of the two player's set of three comes up (it has to come up in order) - this player gets a point. Play first to ten (you keep the same set of three coin tosses).

To clarify, say the first player picks HTH, and the second picks THH, and then the coin tosses are HHTTHTH then the first player gets a point. Then if the second time the coin tosses are TTHH then the second player gets a point.

Hopefully you now understand the game. The puzzle is to find a winning strategy for the second player (one definitely exists) - obviously since there is a random factor it doesn't guarantee victory, rather over time the second player will win more than the first player.
09-30-2009 at 10:02 AM
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jbluestein
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My strategy would be to:

Click here to view the secret text


Josh

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09-30-2009 at 12:21 PM
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Nuntar
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:P I posted that exact strategy, then deleted it when I realised the flaw.

Click here to view the secret text


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09-30-2009 at 01:01 PM
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Nuntar
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Okay, here's a winning strategy, though it's rather clumsy since I had to take each case separately.

Click here to view the secret text


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09-30-2009 at 02:05 PM
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jbluestein
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Nuntar wrote:
:P I posted that exact strategy, then deleted it when I realised the flaw.

Click here to view the secret text

Click here to view the secret text


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09-30-2009 at 02:21 PM
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DanielFishman
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Nuntar has it (though jbluestein was very close).
There is a way of expressing that strategy more simply, though.
09-30-2009 at 03:10 PM
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Maurog
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Click here to view the secret text


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09-30-2009 at 03:19 PM
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brian_s
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It has been two weeks since the last puzzle, so I am interjecting a puzzle of my own:

Five points on a plane are chosen so that no three are colinear. Prove four of those points form the corners of a convex quadrilateral.
10-14-2009 at 01:48 AM
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The Stew Boy
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icon Re: Puzzle "tag" (+1)  
I'm not sure if this is the solution you want, but here's my idea:
Click here to view the secret text


I hope in there's some sense in my ramblings here.
Also, I don't have a puzzle myself, so if I get this right, anyone else is free to post one.

[Last edited by The Stew Boy at 10-14-2009 04:37 AM]
10-14-2009 at 04:29 AM
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brian_s
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Sorry I did not reply earlier. Your solution is a correct solution.
10-18-2009 at 12:21 AM
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brian_s
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Another puzzle, related to the last one.

Find a way to place eight points on a plane satisfying two restrictions:
-1- No set of three points is colinear
-2- No set of five points forms a convex pentagon
10-19-2009 at 08:26 PM
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The Stew Boy
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icon Re: Puzzle "tag" (+1)  
Is it this?
Click here to view the secret text


[Last edited by The Stew Boy at 10-20-2009 07:05 AM]
10-20-2009 at 07:05 AM
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brian_s
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Yes it is!

These last two problems are part of the Happy Ending Problem.
10-20-2009 at 11:10 PM
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The Stew Boy
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Oh. I swear I didn't google them though! I swear!
10-21-2009 at 04:51 AM
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brian_s
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The Stew Boy wrote:
Oh. I swear I didn't google them though! I swear!
Don't worry, I believe you. I chose those two cases because they were easy enough for an average math-inclined person to work out without trouble.

And now, another puzzle: Find a set of four consecutive six digit numbers which satisfies the following:

- The last four digits of the first (smallest) number form a palindrome.

- The last five digits of the second number form a palindrome.

- The second through fifth digits of the third number form a palindrome.

- The fourth (largest) number is a palindrome.
10-25-2009 at 12:39 AM
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Ravon
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Nice puzzle.
Click here to view the secret text

10-25-2009 at 01:50 AM
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DanielFishman
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Another solution:
Click here to view the secret text

10-25-2009 at 09:26 AM
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brian_s
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The two of you got both solutions. I guess either one of you can post the next puzzle
10-27-2009 at 01:30 AM
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Ravon
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Go ahead Daniel. I am puzzleless.
10-27-2009 at 03:28 AM
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brian_s
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It has been a week and a half, so I'll pull another puzzle from my pile.

1) Find a word with the five vowels a,e,i,o,u appearing in that order, not necessarily adjacent to each other. None of the five vowels should be repeated. For example "enough" has e,o,u in order with none of e,o,u repeated.

2) Same as part 1, except the order is u,o,i,e,a.
11-05-2009 at 05:53 PM
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Nuntar
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I know the answers to both parts, but I've seen this puzzle before so I won't spoil it :)

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11-08-2009 at 05:17 PM
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12th Archivist
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The first part I know. If you considering the same word I am considering, there could be an extra challenge by making the order (secreted for the possible chance of someone figuring it out):
Click here to view the secret text


Don't remember a word that fits for the second part.

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11-08-2009 at 07:53 PM
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Znirk
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Click here to view the secret text


... not the kind of thing you were looking for? Well, it helps if you state your requirements :)

OOookaayy. I'll try again:

Click here to view the secret text


[Last edited by Znirk at 11-11-2009 10:45 AM]
11-11-2009 at 10:42 AM
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Nuntar
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Znirk wrote:
... but both of these are cheating a little: the first has a digraph and thus contains only four vowels*
Phonologically it has only three vowels, since the i is also part of a digraph (ti = ch), but it contains all five orthographic vowels which is what was asked for.

The word I know for part two is
Click here to view the secret text


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[Last edited by Nuntar at 11-13-2009 09:11 PM]
11-13-2009 at 09:09 PM
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noma
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Been filling in a lot of blanks in my downtime lately, so here's one more for each:
Click here to view the secret text

11-15-2009 at 06:08 AM
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noma
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I know others answered the previous puzzle first, but it's been a while and I've got a puzzle I'd like to share.
--------------------
On the first day of the Philosophy of Science course, the professor asked his students to tell him why they were there. Most said they needed a humanities course and Ethics for Science was full. The professor laughed and said, "Well, I hope you'll find this course interesting. And I know that what you learn here will influence the way you think. Philosophy is the study of those questions man has been asking for millennia. Questions like: why are we here? What is "here"? For that matter, who am I? And what's it all about anyway?"

"42!" offered a student in the first row.

"Funny. But okay... you're all science and math majors, so you like numbers, right? Here's some for you." The professor turned around and wrote the following on the whiteboard: 53 90 53 7 19 90 68E 9 8 75 53 95.

"Extra credit for the first one who can tell me what it means. In the meantime, let's start with why philosophy is important to science...."

[Last edited by noma at 11-21-2009 08:58 PM : Adjusted puzzle a bit]
11-20-2009 at 08:33 PM
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stigant
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No idea what the answer is, but I took a Philosophy course in High School in which the professor told this story:
You wake up alone, and with no memory, in an apartment with a couch, a small kitchen, a bedroom etc. You have no idea where you are, who you are etc. You start to ask the big questions: "Who am I? Why am I here? Where is here?" etc etc. Eventually, you run out of big questions and ask "Is there any beer in the fridge?"

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11-20-2009 at 09:18 PM
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noma
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"No solution yet?" the professor observed after a few days. "All right, here's a hint. Although most of you are science or math majors, the key to this puzzle might be more easily found by a certain type of science student."
11-26-2009 at 07:50 PM
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TripleM
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Click here to view the secret text

11-26-2009 at 09:22 PM
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noma
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And TripleM has it.
11-27-2009 at 12:35 AM
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