# Thread: Anybody like puzzles?

1. ## Anybody like puzzles?

My girlfriend gave me a really cool book for Christmas called 1000 Play Thinks. It is loaded with a variety of cool thinking puzzles, and I thought that I would share some of the better ones as I went through it.

1. Gloves in the Dark - difficulty rating: 6 out of 10
There are twenty-two gloves in a drawer: five pairs of red gloves, four pairs of yellow and two pairs of green. If the lights are out and you select the gloves in the dark, how many must you choose to ensure that you have at least one matching pair?

2. 2. Halving Seven - difficulty rating: 6 out of 10 (I think it is harder)

7+7=12?

Can you prove that 7 is half of 12?

3. :withstupi

4. 3 guys walk into a hotel room, they each pay \$20 to get in. The manager finds they paid an extra \$8. He sends a hop to the room to return the money. He then keeps 2 dollars,(Realizing he can't divide the money up evenly between 3 people) he gives each one \$2. They each effectively only payed 18 for the room itself then, because 20-2=18. Then they will pay 2 for the hop
They payed 3*18+2=56, u can also say they only payed 52+2=54
(DUH, the room itself cost 52+the bell hop) they obviously paid the same, so 56=54
Then, subtract 42 from each side. 14=12, 14=(7+7)
7+7=12 BIATCH.

5. Hey is there a level 10 in that book?

6. Originally posted by nejar462
3 guys walk into a hotel room, they each pay \$20 to get in. The manager finds they paid an extra \$8. He sends a hop to the room to return the money. He then keeps 2 dollars,(Realizing he can't divide the money up evenly between 3 people) he gives each one \$2. They each effectively only payed 18 for the room itself then, because 20-2=18. Then they will pay 2 for the hop
They payed 3*18+2=56, u can also say they only payed 52+2=54
(DUH, the room itself cost 52+the bell hop) they obviously paid the same, so 56=54
Then, subtract 42 from each side. 14=12, 14=(7+7)
7+7=12 BIATCH.
sorry, nejar - when you say that they payed 3*18+2=56, that would be incorrect. They actually paid 3*18=54 ; the two dollars for the bellhop is already accounted for. If the bellhop had not kept the \$2 and had divided the \$8 three ways, then the 3 fellas would have paid 17.333*3=52.

So 56 does not = 54, 14 does not =12, and therefore you have not shown 7+7 to be = to 12. Nice try, though.

Next!

7. Originally posted by nejar462
Hey is there a level 10 in that book?
Yes, there are a few - most are picture puzzles, but here is one that is not:

3. Flip Fraud - difficulty: 10 out of 10

You ask a friend to flip a coin 200 times and record the outcome. When you are given the results, you want to know whether your friend really flipped the coin all those times or just faked it.
How can you check the results to see whether they are genuine?

8. I will go with 5 gloves must be chosen to ensure a pair.

9. lol, u can sorta prove that 7+7=12 but obviously there will be a counter to that logic lest your blow up time or something

10. "sorry, nejar - when you say that they payed 3*18+2=56, that would be incorrect. They actually paid 3*18=54 ; the two dollars for the bellhop is already accounted for"

Its not really accounted for, because if they u split up the \$8, the \$2 goes to each guy, so each guy pays 2 dollars less effectively giving away the \$2 to the bellhop. So the \$2 isn't accounted for, because they started paying 20*3, becomes 18*3, which later on becomes 18*3+2=56

11. ## Re: Anybody like puzzles?

Originally posted by Craig James
My girlfriend gave me a really cool book for Christmas called 1000 Play Thinks. It is loaded with a variety of cool thinking puzzles, and I thought that I would share some of the better ones as I went through it.

1. Gloves in the Dark - difficulty rating: 6 out of 10
There are twenty-two gloves in a drawer: five pairs of red gloves, four pairs of yellow and two pairs of green. If the lights are out and you select the gloves in the dark, how many must you choose to ensure that you have at least one matching pair?
first of all you split them into lefts and rights

five left red
five right red
four left yellow
four right yellow
two left green
two right green

then you just see what the suckiest thing is that could happen
you take a right green first.
then you take all but the 2 left greens.
and only then you take a left green.

you have grabbed 21 times.

21 times is the max youll have to grab

12. Originally posted by Craig James

3. Flip Fraud - difficulty: 10 out of 10

You ask a friend to flip a coin 200 times and record the outcome. When you are given the results, you want to know whether your friend really flipped the coin all those times or just faked it.
How can you check the results to see whether they are genuine?
You cant really. but if its roughly 50% heads and 50% tails its an indication that it might be right.

you could also look for any patterns in the sequance. if its every time heads then tails most likely its not true.

any fixed pattern in it shows that it is most likely false.

there is no way to be sure.

you could see if he has a sore thumb from flipping it so often if you want to be a smartass.

13. I was going to guess 4 on the gloves, but I hadn't accounted for left or right. Maybe mittens.

I believe heads comes up a few more percentage points than does tails. So if he said it was 50/50 then he didn't really do it.

14. that difference would be too small to draw conclusions by at 200 gos

15. Originally posted by Delphi
I was going to guess 4 on the gloves, but I hadn't accounted for left or right. Maybe mittens.
I had initially guessed 4, like you, Delphi, and we would be right - if we were talking about socks. The fact that there are left and right gloves makes it a little bit tougher.

16. Originally posted by nejar462
Its not really accounted for, because if they u split up the \$8, the \$2 goes to each guy, so each guy pays 2 dollars less effectively giving away the \$2 to the bellhop. So the \$2 isn't accounted for, because they started paying 20*3, becomes 18*3, which later on becomes 18*3+2=56
let me clarify my point a little bit on this one. The total amount spent initially was \$60, or each paid \$20. They overpaid by \$8, so the total that they should have paid was \$52, or \$17.333 each. The bellhop should have given them back \$8 split three ways, or \$2.667 each, which would have meant that the total spent would still be \$52. Instead, the bellhop kept the \$0.667 from each of the 3 guys which adds up to \$2 for him, and means that each guy spent not \$17.333 each, but instead \$18. That is where the \$2 is accounted for. Instead of paying \$17.333 * 3 = 52, now the bellhop has kept the \$2 out of their change, and they paid \$18 * 3 = 54.

As for the the original question of proving that 7+7=12, there is a solution...

17. ## Re: Re: Anybody like puzzles?

Originally posted by Reinier

first of all you split them into lefts and rights

five left red
five right red
four left yellow
four right yellow
two left green
two right green

then you just see what the suckiest thing is that could happen
you take a right green first.
then you take all but the 2 left greens.
and only then you take a left green.

you have grabbed 21 times.

21 times is the max youll have to grab
We are looking for the least amount of times that you would have to grab a glove - but you are on the right track.

18. Originally posted by nejar462
lol, u can sorta prove that 7+7=12 but obviously there will be a counter to that logic lest your blow up time or something
Exactly...I've seen your proof as it's own puzzle before. Since
12 really =/= 14, then there is always going to be a hole in the logic.

19. Originally posted by Craig James
As for the the original question of proving that 7+7=12, there is a solution...
But the point is that since 12 =/= 14, then there is always going to be something fudged in the proof to make it so.

20. Originally posted by Reinier

You cant really. but if its roughly 50% heads and 50% tails its an indication that it might be right.
This was the line of thought that I went along, but it turns out that this is not how you would prove it.

you could also look for any patterns in the sequance. if its every time heads then tails most likely its not true.

any fixed pattern in it shows that it is most likely false.
You are actually in the ballpark here, but not how you think.

you could see if he has a sore thumb from flipping it so often if you want to be a smartass.
Hehe, thats a good thought!

21. Originally posted by NateDogg

But the point is that since 12 =/= 14, then there is always going to be something fudged in the proof to make it so.
Some of the questions need for you to expand your thinking and creativity a little to arrive at the solution. Don't get me wrong, nejar's solution was very creative and fun, but there is an actual way to show that half of 12 is 7...

22. The coin one got me pretty damn stumped, I dunno about it, the only things i could think of were pretty damn ridiculous, like lie detector tests, I could see the pattern thing, but how would u be absolutely sure he wasn't just in a weird coincidence, hell its possible to get heads everytime it just aint likely.

23. U could give him a trick coin, since u'd know that a trick coin would land hands most of the time if he really flipped it he would get heads all the time, and very few if any tails, Still u couldn't be absolutely sure.

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