Interview Logic Riddles/Teasers

1. 9^9
2. You light the match first

Nice triple post

my bad

Why would you not count ^ as a mathematical symbol?

And if "the match" is really the answer to that question, I'd only hire people who got it wrong. I wouldn't want someone that pedantic working with me.

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"It is a fine thing to be out on the hills alone. A man can hardly be a beast or a fool alone on a great mountain." - Francis Kilvert (1840-1879)

"Ce serait bien plus beau si je pouvais le dire à quelqu'un." - Samivel

Agree with the stupidity of the match question. Bear in mind for the first one, you don't need a carrot when writing an exponent (except on a computer).

Got it (re: the carrot)

One more point... if you're going to be that pedantic about the match question, you'd have to define the word "number" a lot more precisely than that.

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"It is a fine thing to be out on the hills alone. A man can hardly be a beast or a fool alone on a great mountain." - Francis Kilvert (1840-1879)

"Ce serait bien plus beau si je pouvais le dire à quelqu'un." - Samivel

That's retarded. If you don't count exponents as a mathematical symbol, I would just write two sideways eights. Infinite times infinite = infinite.

the answer for 1 is infinity;
the first number is
99999999999...9
plus the second number
99999......9

two zeros...intersecting each other in a tangent like fashion to form infinity, of course infinity times infinity is not valid mathematically just as infinity divided by infinity isn't.

You have to remember that infinity is not a number; it's a mathematical concept.

Here's another answer for one:

99. My explanation: It's the two largest single digits put together and I didn't feel like trying to be a smart ass.

i first thought 99 as 2 numbers, and then "100" is two numbers (one and zero). so using that logic it could be 999...998 i guess.

I think we all agree it's a pretty stupid question.

For the interviewers out there, what do you look for when you ask a brain teaser question (even if it's better than this one)? Is it the right answer, the candidates "way of thinking" or just to see that the person doesn't panic??

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"It is a fine thing to be out on the hills alone. A man can hardly be a beast or a fool alone on a great mountain." - Francis Kilvert (1840-1879)

"Ce serait bien plus beau si je pouvais le dire à quelqu'un." - Samivel

Match question is a pretty bad measure of thought process in my opinion. I got this one once... it's an interesting interview question.

There is a lily pad in a pond. (It is the only thing in the pond) It doubles in size every minute and completely fills the pond at 60 minutes. At what minute is the pond 1/4 full?

It should be 1/4 full at the 58th minute.

The pond will then be half full at minute 59, and completely full at minute 60

3) Your name

4) 1.. but if you ask this in an interview, it's hard to tell if you're talking about birthdays or birth days.

largest number: 1/0 = infinity

Really, it's the limit of 1/x as x->0+ that equals infinity. 1/0 itself undefined. Hey, as long as your interviewer doesn't know that I guess its an okay answer...

Question three has many answers, depending on what you classify as yours. Name is probably the best answer to go with, unless you speak in third person all the time. Also, I would think your phone number, being that you do not call yourself. But then you would probably have someone say, "that belongs to your phone, not you." Same goes with your address. Social Security number belongs to you as well, but its usually used by others as a way to identify you. The list could probably go on for awhile.

5) When they meet they are at the same point - same distance away from Paris.

6) Uhh 8 hours? Must be some trick..

6 - I'd imagine the boat continues to rise as it rains more and the ladder will never be half submerged.

Questions 1 - 4 are terrible questions.

Not sure if this is a teaser, but I got this:

You have a 9x9x9 Rubik's cube that you decide to dip in red paint so that when dried all the outside is covered in red. You then throw the all-red cube against the wall and break the 729 cubes that comprise the 9x9x9 completely apart. How many of the pieces will have no red on them whatsoever?

A rubiks cube is 3x3...... but if you insist on a 9x9x9.... 9x9x9 has 6 sides of 81... which is 486 pieces with red paint on them.

all of the side pieces would have paint whether it be painted on 1,2,or 3 sides.
so you're left with a 7x7x7 cube of unpainted little cubes. 343 cubes.

a little bit of a twist on the question:
What is the expected value of the number of painted sides you'd expect if you picked one cube at random?

Now what if you picked 3 cubes?

I didn't "insist" anything. That was the question I was asked from a MM analyst during an interview. I know a Rubik's is 3x3...Bear Stearns gave me one during final round interviews (ha! nice memorabilia).

343 cubes are correct. The reverse engineering way to think about this question is simpler.

Got this one once.

1)You have three 5's and a 1. Using the mathematical operations and all four digits, get to a total of 24.

2)If you have a 5yr bond with a coupon of 5%, and all rates drop to 0%, what would you pay for the bond?

3)This was asked to me in an office: "I make a stack of quarters which stretches to the height of the empire state building. If I took those coins and put them in this office, make me a market in what percentage of the room would be taken up".

4)There is a mile of railway track. It is bolted down in such a way that when it cannot displace to the side but only up or down. If on a hot day, the track expands by one foot, how high up into the air would the rail lift?

Jimbo

1)You have three 5's and a 1. Using the mathematical operations and all four digits, get to a total of 24.
- (5!)/(5/(1^5)) = 120/5 = 24

3)This was asked to me in an office: "I make a stack of quarters which stretches to the height of the empire state building. If I took those coins and put them in this office, make me a market in what percentage of the room would be taken up".
- empire state building about 1000feet tall, room is about say 10x10x10. quarters have diameter of 1 inch. could either use area of quarter or length of quarter to calculate how much of the room would be occupied. using area: so area of quarter is about .75 sq. in. so, the total volume of the stack is 1000 x 12 x .75 = 9000 cubic inch. total volume of room is 120x120x120 so about 1.7 mil cubic inches. 1700/9 is about 200 so approximately .5% of the room. using length method: we know stack is 12000 inches tall so we could divide this stacks into stacks of height 120, so we'd need 100 stacks. the room is 14400 stacks wide, so 100/14400 is about 1/144 or .7% of the room.

have an exam in a bit, will try the others after.

(5 x 5) - 1^5

(5x5)^0.5x5-1=24
:)

the bonds question anyoone ???

the empire estate building question... i had the same answer more or less, quite impressed that the actual % is quite low....

For the bond question wouldn't the market price be $1,250? If rates are at 0% you would just pay out all the future cash flows at the start of the bond's life.

Of course that answer would not take into account inflation, time value of money, alternative investments, etc. etc.

Clarification on #1, only the four primary operations are open to you, exponents are not allowed.

sure it would. 125 price is correct.

for #3 there is a much faster way of approaching it. the office was on a single floor, one story high. keep that in mind.

It depends on what set of numbers you're working. Infinity is a number in the extended real number system. Of course, this set does not form a field, but it is still widely used.

any more brainteasers?

(5-1/5)5

1) You are on a gameshow, behind one of the doors is $1000. Behind the other 2 is nothing. You pick a door. The host, opens one of the other doors, revealing that it's empy. What would you pay to switch?

2) Well, this one is tougher and maybe too involved for this forum but...assuming you have a swap curve built through the 30 yr point, and nothing beyond that, make me a market in a 40yr/50yr rate switch.

3) I have two envelopes. One contains twice the amount of the other. I give you one of the envelopes. Should you switch?

Jimbo.

well done

I heard this from a friend:

you play a game in which a deck of cards (52 cards) will be revealed to you one after the other, before each card is revealed you can make a bet about whether the card is red or black. You start off with x amount of money. For each bet you can use any fraction of your money (assume x is infinitely divisible), if you win, the money you bet gets doubled, if you lose you lose all the money you put into the bet. You play this game until all 52 cards are revealed. What strategy should you use to maximize a riskfree(!) outcome.

Jimbo, if you asked me #3 in an interview I would reply the following:

If you are on the second floor a building, and you have a stack of quarters the height of the empire state building, and you begin to place all the quarters into the single room, by the time you would finish there would be no quarters in that room. Reason being, the floor would collapse beneth the quarters due to the weight. Therefore, the answer is zero.

"Reason being, the floor would collapse beneth the quarters due to the weight. Therefore, the answer is zero."

And you would be very wrong.

Count and wait until you know that only one color remains in the deck, and then bet. I thin that's the only way you hit the risk free criteria. Or at the least, wait until two cards are left and bet half.

Ah, it was worth a shot. It was the first thing that came to my head when you emphasized that the room was on the second floor.

but apparently it's wrong...

ANSWER TO:

1. I would pay nothing becuase the probability is in my favor now. So why pay money to switch.

1) EV of the envelope that you have in your hand is $333.33. EV of the other envelope is $500 so I'd be willing to pay $176.66 or less.

Ok Tyler, and now that you've switched, i give you the chance to switch again. Would you do it?

Think again, it's definitely advantageous to switch. Let me phrase the question again.

There are three doors on a gameshow. One has $1000 behind it, the other two have nothing. You pick one. The host opens one of the two remaining doors, revealing its contents to be empty. He now gives you a chance to switch to the remaining closed door, or keep your original choice. What would you pay to switch?

i could be way off, but i'd be willing to pay any amount up to $666.67 to switch doors. my reasoning is this: the chances of my initial choice being a door with nothing behind is is 2/3, whereas my chances of choosing the $1000 door right off the bat is only 1/3. logic would dictate that more often than not, i'll choose a losing door on my first try. the fact that the gameshow host always reveals an empty door is the key to this question. 2/3 of the time (when you pick a loser right off the bat) he'll reveal the second loser leaving you the option to switch to the winning door, compared to the 1/3 chance of you picking a winner the first time around and the host revealing only one of the losers (leaving you the option of switching to another loser). so, by only paying up $666.67 i "guarantee" that i leave the show with no less than what i started with, or in the best case scenario (assuming i pay between 0 and $666.67) anywhere between $333.33-$1000.

also, is the answer to the expanding one-mile railroad question 51.38 feet, jimbo?

yes to the second.

for the first, you already have something with an expected value of 333, so to switch to something worth 667 or so, i'd think you just pay the difference.

What are your thoughts on my switching envelopes. I have two envelopes. You pick one, and open it, revealing the contents. I tell you the one envelope contains twice the amount of money as the other. Do you switch?