### Brain Teasers

# Counting to 50

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?

"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.### Answer

She wants to say, "6."The series of numbers she will say is 6, 17, 28, 39, 50.

Since she wants to say 50, she needs Henry to say a number between 40 and 49. Therefore, she wants to say 39.

Knowing she wants to say 39, she needs Henry to say a number between 29 and 38. So she wants to say 28. Following this same logic recursively, she will want to say 17, and she will want to say 6 to start the game, and be assured victory.

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## Comments

Jan 11, 2005

good one

I really wanted to get this one and it took me some time. Excellent!!

Nice

this was a 5 star teaser

I like your teaser I saw something like that on tv once.

Jan 20, 2005

isnt it possible to beat her if i say 15?

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 liked it, but it was a bit easy. I play these kinds of games all the time. Kepp up the great teasers.

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!

I like this teaser! This one is definetly going into my Favorites!

CUTE!!

one of my favorites, great job.

U sure stumped me! Nice one!

I LOVED IT!!!!

i wuz stumped until i read the hint

make sum mor!!

i wuz stumped until i read the hint

make sum mor!!

wonderful

I suck at math, so I didn't get this. But I like this kind of puzzle, so:

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!

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...

I've played the 21 game too, but you WIN if you get to 21... very nice, though, finally a tough one!

I liked this one and was able to solve it easily .

awesome! i'm gonna play that game now, cause i'm sure to win!! keep up the good work!!

Good job! One thing though: The words "at least" leave too many possibilities. It could have worked out differently.

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.

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.

why not just say 50?

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..."

Smart

i found it easy

no seriously

no seriously

how am i supposed to know?????????????

just say 50 and you win

Good thought provoking teaser. i didn't get it right either. Thanks for posting.

i didnt even try! i like the answer of just say 50....lol

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.

Very easy. 50-(11+1x4)=6

I meant 10+1x4

NICE!!!

Tough but fair! Thanks

Great quiz!

But, I don't do numbers...

But, I don't do numbers...

Like anybody would actually play that game in real life.

Nice puzzle! I had to work it backwards also. :-)

What can I say? This was easy for me, a nim expert.

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!

good teaser btw!

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!

6, "and at most 10 higher" is 16

NOT 17...

Maybe I'm just tired but it doesn't make sense to me!

Just say 50 Gretchen!

That was my solution too BookWorm. Did the rules say we couldn't say 50 right off the bat?

Opps nevermind, yes it did, you had to start with a number between 1 and 10.

AROB. Still easy

Ok, if she says 10, then he says 11 âˆ’ 20, then she can pick 21, he 22 âˆ’ 31, her 32, him - 33 âˆ’42, her - either 39 or 50 depending on his pick.

Isn't this a possibility as well?

And doe - please translate arob???

(=

Isn't this a possibility as well?

And doe - please translate arob???

(=

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.

guess I need more coffee!

great teaser. Something to amuse my kids!!

I am not good at figuring these things out. I just assumed if she started out saying ten, then he would add ten and then she ten etc. until she said 50. That was my easy solution. He might not say the ten each time tho and there goes my theory.

I started backwards, too. Easier that way I figured.

I did it that way, too, Catmom. That's the way I think. I did get 6. fun puzzle.

If G says 10 then H will have to say a maximum of 20 and G will say a max of 30 then H will say a max of 40 G will win ?

NiCe OnE bRo :3

Very good teaser! Good explanation as well.

I was never very good at math. Some things never seem to change! I lose my patience with myself if I don't get it right away. This was a teaser I will have to try on my husband, who is good at math.

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