# Mike's Riddles

• June 12, 2016 at 7:04 pm #1995
Mike Kim
Keymaster

So, as some of you may already know, I love riddles — (not puns — I do not like puns) —

And I figured that, since studying for the LSAT isn’t frustrating enough, I ought to distract you with some additional challenges —

So, here’s a thread to which I will periodically be adding some of my favorite riddles —

Here is the first one — hope you enjoy it, and if any of you have a riddle to share I’d love to see it! —

Kids Next Door

So, you have a new family moving in next door to you, and all you know about them is that they have two kids. You see one of the children and it is a girl. What are the odds that the other child is also a girl?

Please note again that there is no play on words, no trick about what constitutes a family, and so on — it’s straight-up just math.Enjoy!

• June 12, 2016 at 9:30 pm #1996
LSAT Dan
Participant

Straight-up math with numerous applications, including one of my favorites. Let me just say that no good serious bridge player would miss that one (and it’s a great one, Mike).

No spoilers from me, though.

But on a related note…I roll two (6-sided) dice behind a screen with the agreement that as soon as a “1” comes up on (at least) one of the dice, I’ll reveal a die with a “1” showing. When that happens, I ask you if you’d like to bet on whether or not the other die also shows a “1”. Of course, since there are more “non-1s” than “1s,” I’ll have to give you money odds. And the fair (breakeven) odds for me to give you are…?

From the straight-up math to the straight-up physics:

You and a brick are in an inflatable raft, floating in a swimming pool. You toss the brick overboard, and it sinks to the bottom of the pool, without damaging the integrity of the pool. Does the water level in the pool go up ever-so-slightly, go down ever-so-slightly, or remain exactly the same?

And lastly, a little straight-up geography:

You’re in a balloon, directly over the center of Detroit, Michigan. You start to travel due south. What’s the first foreign country you’ll pass over?

Speaking of traveling due south…Straight-Up Geography, Part Deux:

You’re out hiking. You travel a mile due south. Then you travel a mile due west. Then you travel a mile due north. You find yourself exactly where you started.
Keeping it 2-dimensional (i.e. you’re on the surface of the earth, not floating above or tunneling below it)…How many points on the globe are there where you might be?
(careful)

• June 12, 2016 at 9:40 pm #1997
LSAT Dan
Participant

BTW…we’re going to have to talk about the girl next door riddle; as I’m sure you know, it’s got a more famous ‘twin’ riddle, but they’re more fraternal than identical…

• June 13, 2016 at 10:25 am #1999
Mike Kim
Keymaster

So at this point I
a) have wasted the last hour on Dan’s riddles when I should have been working instead.
b) am very happy to have Dan contributing regularly on this site.
c) am slightly nervous the level of nerdiness we continue to exhibit together may scare off the cooler kids.
d) feel a bit like salieri to dan’s mozart (without the bitterness), when it comes to riddles and perhaps everything else as well —

• June 13, 2016 at 11:19 am #2000
LSAT Dan
Participant

a) is hilarious
b) is great to hear
c) is understandable
d) is ridiculous

Always good to connect with people who find stuff like this fun or interesting!

• June 13, 2016 at 12:06 pm #2001

Cute, guys, cute.

• June 14, 2016 at 1:03 pm #2014
LSAT Dan
Participant

The king’s daughter had three suitors. Being a king in a riddle, the king decided to handle the situation in the time-honored way; he would allow one of the suitors to marry the daughter, and he would possibly kill the other two. He blindfolded all of the men, and lined them up, facing the same direction, so the one in the back could see he other two, the one in the middle could the one in front of him, and the one in front of him could see nothing. Their heads were strapped down so their views could not change.

All of the men were quite intelligent and motivated, after the king explained the situation. The situation was this: While they were blindfolded, the king had chose three hats at random from a bag of five: two blue, and three red. Each of the chosen hats was placed on one of the suitor, and each suitor was given a chance to guess what color his hat was. Guess right, you get the princess; guess wrong, you get beheaded. Choose not to guess, you get returned to your regular life. All of the suitors wanted the princess, but none wanted her enough to take on a non-zero chance of being beheaded (which is math-talk for, “Nobody was guessing unless he was certain.”)

The king said, “Because I like you most, Adam, I’ve not only placed you in the back where you can see the other hats, but I’m also going to let you go first!”

Adam cleared his throat and said, “I have no guess to make.”

The King said, “Because I like you more than I like Charlie, Bernard, I’ve not only placed you in the middle, where you can see Charlie’s hat, but I’m also going to let you go second.”

Bernard cleared his throat and said, “I have no guess to make.”

The King said, “My daughter likes you, but I hate you, Charlie, so I’ve placed you in the front and let the other suitors have their chances before you got yours.”

Charlie cleared his throat and said….what?

• June 14, 2016 at 1:25 pm #2015
LSAT Dan
Participant

By the way, the King’s Daughter’s Suitors riddle is 100% directly applicable to LSAT prep, and everyone reading it is capable of figuring it out.

• June 14, 2016 at 2:09 pm #2018
Mike Kim
Keymaster

Re: King’s daughter

Wow, is that a satisfying one! I’ve seen a different version before (maybe 2 of each color or something like that?) — but I love this version! And no physics or geography involved!

• June 14, 2016 at 4:26 pm #2019
LSAT Dan
Participant

Yeah, it’s one of my favorites, Mike. Very…? Clean?

C’mon, LSATters…give it a crack! I’ll start it for you:

“If _______________, then Adam would have known what color his hat was.
Adam did not know what color his hat was; therefore, _________________.”

• June 14, 2016 at 9:28 pm #2024
feelinglawful
Participant

I have to say 50%. Just because the first child I notice is a girl, that shouldn’t affect the other child’s chances of being a girl as well. Am I right?

I can’t help but wonder if I’m missing something!

• June 15, 2016 at 8:39 am #2035
Mike Kim
Keymaster

Ha — cause if it was that straightforward, it wouldn’t be a riddle, right?

So, normally, I would confidently say the answer I always thought was correct, which is 1/3.

However, off the forum, Dan actually showed me that, per the way I happened to state the situation, the right answer is actually not 1/3 (Dan, if I understand u correctly, the right answer actually is 1/2, right?).

Now, if u can figure out how I (i.e. Salieri) got to 1/3 or how Dan (i.e. Mozart) got to 1/2…

• June 15, 2016 at 9:26 am #2036
LSAT Dan
Participant

These riddles (specifically, the ones about the boys and the girls) are very subtle and multi-layered. Yes, FeelingLawful (and Mike), you’re correct…it’s 50%; on the other hand, seeing the one girl DOES change quite a bit. It just happens to change things in ways that completely balance out and leave the chance at 50%! As an example of the subtlety, though, let me give you a slight variation of the riddle.

One day, Mike told the riddle in the initial post. Dan, hearing the riddle, said, “The chance that the other child is a girl is 1/2, not 1/3! I’ll even put a little wager on it. I know who lives in every house in Tustin, and I know that you don’t know anyone in Tustin, so you pick a random street, and we’ll go to the first house on that street that has two children living in it, unless the children are both boys. To match the riddle, we can only use houses that have at least one girl.

If the house has TWO girls, you give me \$5, but if the house has a boy and a girl, I’ll give you \$4.”

If the chance that the other child is a girl is 1/2, then Dan has the good part of the bet – half the time, he gets \$5; half the time, he gives up \$4.

If the chance that the other child is a girl is 1/3, then Mike has the good part of the bet – he gets \$4 twice for every one time he gives up \$5.

And even though the answer the original riddle was 1/2, after they repeated this little bet for a few hours, Dan ran out of money…because now the chance was actually 1/3.

Say what?!

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