Braingle: 'Counting to 50' Brain Teaser

Counting to 50

Logic puzzles require you to think. You will have to be logical in your reasoning.

Puzzle ID:	#20287
Fun:	(2.91)
Difficulty:	(2.37)
Category:	Logic
Submitted By:	tsimkin

Henry and Gretchen are going to play a game. Henry explains, "You and I will take turns saying numbers. The first person will say a number between 1 and 10. Then the other person will say a number that is at least 1 higher than that number, and at most 10 higher. We will keep going back and forth in this way until one of us says the number 50. That person wins. I'll start."

"Not so fast!" says Gretchen. "I want to win, so I will start."

What number should Gretchen say to start?

Hint

By following this strategy, she is assured a victory. Think of all of the numbers she will want to say.
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Comments

(user deleted) Jan 11, 2005	good one
strangelove Jan 12, 2005	I really wanted to get this one and it took me some time. Excellent!!
mosoh Jan 12, 2005	Nice
eina_23052 Jan 13, 2005	this was a 5 star teaser
God-sGrace2005 Jan 13, 2005	I like your teaser I saw something like that on tv once.
(user deleted) Jan 20, 2005	isnt it possible to beat her if i say 15?
tsimkin Jan 20, 2005	no. if you say 15, she will say 17. then whatever you say, she will be able to say 28. then whatever you say, she will be able to say 39. then whatever you say, she will be able to say 50, and win.
i_am_sam007 Jan 23, 2005	I liked it, but it was a bit easy. I play these kinds of games all the time. Kepp up the great teasers.
(user deleted) Jan 26, 2005	I used to play a game like this called "21." We could say 3 numbers at a time and the first one to say 21 loses. I like this teaser! This one is definetly going into my Favorites!
RoxyChick13 Jan 27, 2005	CUTE!!
chuckelect Feb 09, 2005	one of my favorites, great job.
roseblood003 Feb 11, 2005	U sure stumped me! Nice one!
horseybaby34345 Feb 11, 2005	I LOVED IT!!!! i wuz stumped until i read the hint make sum mor!!
94_8 Feb 11, 2005	wonderful
fuzzie277 Feb 11, 2005	I suck at math, so I didn't get this. But I like this kind of puzzle, so:
marigold Feb 11, 2005	I don't know about everone else, but that teaser was really hard for me. I'm not too great with numbers... Anyway, great teaser!
(user deleted) Feb 12, 2005	new to this site...enjoy it very much....nice teaser,albeit just a tad easy...good though...thats the thing with math...the numbers never lie...keep 'em coming...
melilyn Feb 12, 2005	I've played the 21 game too, but you WIN if you get to 21... very nice, though, finally a tough one!
Raza Feb 13, 2005	I liked this one and was able to solve it easily .
dogfanatic77 Feb 13, 2005	awesome! i'm gonna play that game now, cause i'm sure to win!! keep up the good work!!
itsn06 Feb 15, 2005	Good job! One thing though: The words "at least" leave too many possibilities. It could have worked out differently.
tsimkin Feb 15, 2005	Actually, the words "at least" do not leave too many possibilities. Whatever Henry says after Gretchen says "6", she will be able to say "17". For example, if he said, "12", she would say "17". Then whatever he said next (say, 19), she would say 28. If you disagree, send me a PM. Thanks.
Tree Feb 24, 2005	Very good teaser. I've never seen one like that. It reminds me of a game where you take away marbles in rows that I played recently.
jimmym Sep 10, 2005	why not just say 50?
tsimkin Sep 12, 2005	jimmym -- You don't just say 50 for the same reason that you don't play darts by walking up to the dart board to placing your darts all in the bull's-eye. The game has rules, and the object is to win it while still playing by the rules. "The first person will say a number between 1 and 10..."
jsdodgers Sep 13, 2006	Smart
calmsavior Sep 18, 2006	i found it easy no seriously
kuttiekat2u Jan 14, 2007	how am i supposed to know?????????????
kuttiekat2u Jan 14, 2007	just say 50 and you win
bradon182001 Sep 08, 2008	Good thought provoking teaser. i didn't get it right either. Thanks for posting.
malogalee Sep 08, 2008	i didnt even try! i like the answer of just say 50....lol
auntiesis Sep 08, 2008	That was easy, I started with 50 and worked backwards, just like the answer. It took me longer to figure it out than to read the answer and I needed paper & pen.
doehead Sep 08, 2008	Very easy. 50-(11+1x4)=6
doehead Sep 08, 2008	I meant 10+1x4
UptheHill Sep 08, 2008	NICE!!!
abrain Sep 08, 2008	Tough but fair! Thanks
avonma Sep 08, 2008	Great quiz! But, I don't do numbers...
crystalblade Sep 08, 2008	Like anybody would actually play that game in real life.
dragonlove Sep 08, 2008	Nice puzzle! I had to work it backwards also. :-)
FatHead Sep 08, 2008	What can I say? This was easy for me, a nim expert.
srpwuzhere Sep 08, 2008	hehe me and my friends used to play a game where you would have to count to 100. whoever got there was out and kept going until there was one person left. whoever was left wins :-) good teaser btw!
jentaylor728 Sep 08, 2008	I disagree... 6, "and at most 10 higher" is 16 NOT 17... Maybe I'm just tired but it doesn't make sense to me!
BookwormAnG Sep 08, 2011	Just say 50 Gretchen!
HABS2933 Sep 08, 2011	That was my solution too BookWorm. Did the rules say we couldn't say 50 right off the bat?
HABS2933 Sep 08, 2011	Opps nevermind, yes it did, you had to start with a number between 1 and 10.
doehead Sep 08, 2011	AROB. Still easy
teri12265 Sep 08, 2011	Ok, if she says 10, then he says 11 − 20, then she can pick 21, he 22 − 31, her 32, him - 33 −42, her - either 39 or 50 depending on his pick. Isn't this a possibility as well? And doe - please translate arob??? (=
tsimkin Sep 08, 2011	Teri -- when you say that he can say 33-42, that means he can say 39. If he does, Gretchen is out of luck, since she will then have to say a number between 40 and 49.
teri12265 Sep 08, 2011	guess I need more coffee!
omas Sep 08, 2011	great teaser. Something to amuse my kids!!