Puzzle Quiz

Renata

Renata

homicidal jungle cat
GOTM Staff
Joined
Jan 14, 2003
Messages
7,929
Location
NY
Betazed's logic puzzle in the 'math gene' thread got me thinking how much I like puzzles and riddles. So I thought I'd start a quiz thread along the lines of the others floating around.

Any sort of puzzle or riddle involving logic, wordplay or whatever is allowed; use your judgment on what's a reasonable amount of complexity or math to deal with, but otherwise ask whatever questions float your boat.

Format is the same as the other quizzes. I'll start us off, and whoever answers correctly can have the honor of asking the next quesion.

Here my question; it's another weighing puzzle in honor of betazed's question from the math thread.

You have ten boxes; each contains nine balls. The balls in one box weigh 0.9 kg; the rest weigh 1.0 kg. You have one weighing on an accurate scale to find the box containing the light balls. How do you do it?

Cheers,
Ren

edit: I have to go do some errands, so whoever gets this one can ask the next without waiting for me -- should be self-evident.
 
I take one ball from box 1, 2 from box 2 , three from box 3 and so on and then measure the combined weight of this collection which is W

Then you have .1x + (55 - x)10/9 = W

Solve for x and you know which bag had the odd balls.

:goodjob:
 
Ok. Here is another one.

You have a chessboard. It is 8 X 8 squares. I give you 64 1 X 1 square pieces of paper. You can obviously put them on top of each of the 64 squares and cover the board.

Now instead of that I give you 32 2X1 rectangles of paper. Once again you can line them up covering two sqauers each and cover the chessboard.

Now I remove two corner squares of the chess board so that it is 62 square units in area and give you 31 2X1 rectangles of paper. Can you cover the board now? IF yes show how, if not why not?

hint: when I was asked this I had no clue. but on looking at a chessboard I knew it immediately. I urge you do the same.
 
I would say that it is possible if you remove two corners on one side, and impossible if you remove two opposed corners.
In the first case you can just lay your pieces of paper in "lines", with one line (the one with the two corners removed) having one less slip of paper.
In the second, I cannot think of anyway to do it without having to cut one of the piece of paper in two which is obviously not allowed.
 
Since in the second instance, both of the squares removed are white IIRC, it becomes impossible to cover up one white square and one black square with the pieces of paper, as there are two black squares more than white squares on the board.
 
You are very close Kinniken. Your intuition is correct. Now just make your arguments more precise. :)

edit: I just saw nonconformist posted the right reasoning. :goodjob: Your go!
 
Originally posted by betazed
Now I remove two corner squares of the chess board so that it is 62 square units in area and give you 31 2X1 rectangles of paper. Can you cover the board now? IF yes show how, if not why not?
Click to expand...
Yes, you can. There are many ways you can cover the board, one of which may actually use the paper you give us.
 
Originally posted by nonconformist
A couple has seven children. Half of them are girls. Expalin this.
Click to expand...
"Half of the them" doesn't necessarily mean "half and only half," so if for example six of the children are girls then half of them are girls.

Correct?
 
Originally posted by WillJ
"Half of the them" doesn't necessarily mean "half and only half," so if for example six of the children are girls then half of them are girls.

Correct?
Click to expand...
The problem with some of these is that the words in that question aren't defined very well. Half can also mean exactly half. So if the question were worded with no ambiguities then it would be easy to answer.
 
Well if the question was worded properly it would be 'exactly half of them are girls'. Then the correct explanation would be 'all seven of them are girls.' If all of them are, then obviously half of them are as well. :D I like that one.

Who's next?

Renata
 
All right, here we go:

An enemy submarine is somewhere on an integral number line. It is moving at a rate of integral units per minute. You know neither its position nor its velocity. You can launch a torpedo each minute at any integer on the number line. If the submarine is there, you hit it and it sinks. You have all the time and torpedoes you want. You must sink this enemy sub---devise a strategy that is guaranteed to eventually hit the enemy sub.

[Edit: Corrected a typo.]
 
I was foxed for a moment there WillJ, till I remembered that product of countable sets is a countable set. :D

If the position of the sub is given by A + Bt (where t is time and A and B are integers) then all you have to do is span the countable set A X B. Following is a counting.

(0, 0), (0, 1), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2) .....

:goodjob:
 
I have more fun answering riddles than asking. So I will pass the baton for now on to someone else.

Go ahead and ask.
 
Okay, I suppose I'll ask another one, if that's all right:

Three coworkers would like to know their average salary. However, they are self-conscious and don't want to tell each other their own salaries, for fear of either being ridiculed or getting their houses robbed. How can they find their average salary, without disclosing their own salaries (and without asking their boss :p)?
 
They could each just tell some random other guy, and get him to figure it out. He would then tell 'em the average. Correct?
 
You must log in or register to reply here.

Similar threads

Syterion
Puzzle Quiz #2
36 37 38
Replies
752
Views
25K
Scuffer
Scuffer
GoldEagle
"The CivFanatics Weight Loss Challenge"
2 3
Replies
43
Views
2K
classical_hero
classical_hero
Back
Top Bottom