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Friday's Logic Puzzle

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by cupcake 1 view

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At the company I work, we have a Friday Quiz, in which the boss
sends out to his team a logic puzzle. There are specific rules and his
answer is the final answer. I felt that I answered the puzzle
successfully first, but he did not agree.

I am posting the puzzle (and the rules) here and I'd like to hear other's
answers...

Thanks!
Cupcake

------------------
Here are the rules for today (and they?re different from last time):

1. You may NOT use the Internet NOR may you ask for help from
anyone else; you MUST do your own work.

2. You may ask questions for clarification of the first two paragraphs
of the problem. However, I will only reply to questions that you have
asked by ?replying to all?. In other words, if you want to ask a
question, everyone gets to know the question; and when (if) I provide
an answer, everyone gets to know the answer too. When you have
your answer, submit that directly to me ? you don?t have to copy the
whole team on that one.

3. As usual, the question has been meticulously researched, although
the answer has not. Sticklers for the truth should start their own
game (although I don?t what you?d offer as a prize).

4. I will respond to emails in the order in which they are received.

5. Players who have won recently should sit on their hands and let
someone else have a chance for a change.

6. Ask as many questions for clarification as you want, BUT you may
submit ONLY ONE answer, and the first answer you submit is the one
I?ll go with, even if you submit a second, better answer later. You may
submit questions up until 10:30, and then I will answer all of them (in
other words, I have meetings until then). The game ends at 12:30 at
which time I will declare a winner.

So, here?s the problem for today:

You have 50 white marbles and 50 black marbles. You also have two
large opaque jars that rotate constantly. You may place any number
of marbles of either color in the jars in any fashion you want.

Once you have placed them to your satisfaction, I randomly determine
a jar, and randomly pick a marble from the jar. If the marble is white,
you win a prize. But, if it?s black . . . bad things happen.

So, how do you distribute the marbles between the two jars to
maximize you chance of winning? And, having done that, explain why
(bonus points if you can also give me the probability of winning based
on your solution).

26 replies

by netman1958

His rule:
"You may place any number
of marbles of either color in the jars in any fashion you want."

didn't say you had to put all the marbles into the jars. I would put 1 white marble in each jar and leave the other marbles out.

probability 0f winning: 100%

by cupcake

That was how I answered the question and he said that I
didn't clarify the point and therefore, I lost.

I'm challenging!! ;-) Not really, he is my boss, and you
know what they say, "the boss makes the rules".

His choice for winning answer was:

If you place 1 white ball in Jar #1 and then 49 whites and
50 blacks in Jar #2, this give the best probability of
success.

Use Case #1: Jar #1 is selected randomly; there is only
one ball in there, and it is white, so in this case the
probability of success is 100%.

Use Case #2: Jar #2 is selected randomly. There are 49
whites and 50 blacks, so the probability of success is
49/99 or about 49.5%.

Total probability before knowing which jar is selected is
just about 75%.

by notsochiguy

Of course, I was once disqualified from a corporate event due to strict adherence to the rules (or lack thereof). So take my approval with a grain of salt! :)

We were doing a 'water race relay', where you are given a spoon and need to fill up a glass on the other side . The specific rule read 'take the spoon, and fill up the glass with water'. So, when handed the spoon, I picked up a bottle of water, strolled over with both in hand, and filled the glass up to the brim with the bottle of water.

When the other teams said my team (I) cheated, I simply asked them to point out to me where it said I had to use the spoon to fill up the water (call it the Brady Exact Word defense).

Businesses constantly bemoan the lack of 'out-of-the-box' thinking, but heaven forbid someone actually challenges the prevalent thought pattern!! ;)

by jck

you think different than me.

it said "Once you have placed them to your satisfaction,...", I took that to mean all 100

by shasca

One white in each one seems brutally obvious to me too. How did this guy become boss with logic like that? Did one of his "pets" win the prize?

His solution would have been merited if one of the rules was that you have to use all the marbles. That may have been his mindset, but he did not make it mandatory.

by jellimonsta

If you had to use all, I would pour half black in one jar, then the other half in the additional jar.
I would then pour 1/2 the whites in 1 jar, and the other half in the addtional jar. Being as the white marbles would cover the vast majority of the black, I think that gives a pretty good chance of winning. :p

by shasca

You have 50 white marbles and 50 black marbles. You also have two
large opaque jars that rotate constantly.

I would be worried what rotate means. Could be a tumbling effect on jars contents.

by thumbsup2

(1) Must all 100 marbles be placed in one jar or the other?

(2) Can the Boss shake the jars before making the one marble selection?

If the answer to (1) is no, then the answer to (2) doesn't matter. Placing 1 white marble per jar would be the solution; chance of winning 100%.

If the answer to (1) is yes and the answer to (2) is no, then place 25 black marbles into each jar first; place 25 white marbles on top of them; chance of winning 100%

However, if the answers to (1) AND (2) are both yes and you put 50 marbles in each jar (25 of each color) and the jars can be "shuffled", your chances of winning drop to 50/50. This is where you might use the "winning" answer with 1 white marble in the first jar and the remaining 99 marbles in the 2nd jar. The odds on the first jar are 100%, but the odds on the 2nd jar are 49/50 making your overall odds roughly 75% chance of him grabbing a white marble, I think. Heck, I never have been good at odds! ;)

by w2ktechman

I would have gone for clarification on 2 points. Do all of the marbles need to be added and how are the jars rotated

by jck

Put all the black marbles in one jar...then put all the white ones on top of them.

You have not said that the jar must have at least 1 marble.

by pringles86

If he doesn't find a marble you don't lose. You don't win a prize, but you also don't have "bad things happen". It is sort of a draw.

by jck

White Marble = prize
Black Marble = bad thing

If you write a program and say:

-------------------------------

Do While WhiteMarbleCount < 50
If Marble = White then
Output.write("Prize")
WhiteMarblecount += 1
Elseif Marble = Black then
Output.write("Bad Thing")
BlackMarblecount += 1
Else
End if
Output.Write("Your prize percent is " & _
(WhiteMarbleCount/(WhiteMarbleCount + BlackMarbleCount))*100
End Do

--------------------------------------------

Notice, the game gave no condition for the Else in the rules of the game.

Hence, nothing occurs and they keep going until all 100 marbles are found...even if they reach in the empty jar.

by netman1958

would be:

If Marble = White then
Output.write("Prize")
Elseif Marble = Black then
Output.write("Bad Thing")
Else
Output.Write("No marble picked")
End if
End

by oz_media

Ask him to participate in a grammar quiz; based on the question he provided, he's bound to lose. :D LOL.

by cupcake

...I will try and post them every Friday!

I will be interested to see anymore creative solutions!

Have a great weekend!

Cupcake

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