Brainteasers

What is the largest possible number you can write using only 2 numbers - just 2 numbers, no other mathematical symbols?

9^9

Alive without breath, as cold as death; never thirsty, ever drinking, all in mail never clinking.

A fish

There are 3,182 players in a tennis head-to-head knockout tennis tournament. How many matches must be played to crown a winner?

An important part of this question is that it is a knockout tournament. So if you are looking to crown a winner ALL but one must lose. The only way to lose is to play a match. In order to have a winner you need to have total participates - 1 lose which requires exactly that many games.

How many birth days does the average man have?

One

It's 3:30pm. What is the angle formed by the hour hand and the minute hand?

75 degrees

A scientist puts a bacteria in a petri dish at exactly noon. Every minute the bacteria divides into two and doubles in size. At exactly 1 PM the petri dish is full. At what time was the dish half full?

At 1 pm the dish is full. If bacteria doubles every minute, then one minute earlier, the dish must have been half full. Bob's your uncle; the dish was half-full at 12.59 pm!

How many times a day do a clock's hands overlap?

At first, it might be tempting to just say "24," but the correct answer is "22." This can be surmised because the clock hands approximately overlap at 12:00, 1:05, 2:10, 3:15, 4:20, 5:25, 6:30, 7:35, 8:40, 9:45 and 10:50 twice a day. You will notice that there is no 11:55 because the hands will not overlap at that point because the hour hand is moving toward 12 when the minute hand is at 11.

Here is the question again: "During lunch, 5 of Mr. Bryant's students visit the supermarket. One of the 5, stole an apple. When questioned... Jim said: it was Hank or Tom. Hank said: neither Eddie or I did it. Tom Said: you're both lying. Don said: no one of them is lying, the other is speaking the truth.Eddie said: no Don, that's not true. When the shop owner asked Mr. Bryant, he said that three of the boys are always truthful, but two lie all the time. So - who stole the apple?"

Don and Eddie contradict each other which means one of them must be a liar. One of the remaining boys must also be lying (there are 2 liars). Tom has said 'you're both lying' about the two other remaining boys (Jim and Hank), but there can only be one liar, so it must be him. Jim and Hank are both telling the truth so it can't be Eddie or Hank who stole the apple. Tom must have stolen the apple. (I was suspicious about Jim at first, but if you read carefully, Jim said it was Hank OR Tom - so he's not actually contradicting Hank's words).

You've got a 10 x 10 x 10 cube made up of 1 x 1 x 1 smaller cubes. The outside of the larger cube is completely painted red. On how many of the smaller cubes is there any red paint?

First, note that the larger cube is made up of 1000 smaller cubes. The easiest way to think about this is how many cubes are NOT painted? 8 x 8 x 8 inner cubes are not painted which equals 512 cubes. Therefore, 1000 - 512 = 488 cubes that have some paint. Alternatively, we can calculate this by saying that two 10 x 10 sides are painted (200) plus two 10 x 8 sides (160) plus two 8 x 8 sides (128). 200 + 160 + 128 = 488.

Four investment bankers need to cross a bridge at night to get to a meeting. They have only one flashlight and 17 minutes to get there. The bridge must be crossed with the flashlight and can only support two bankers at a time. The Analyst can cross in 1 minute, the Associate can cross in 2 minutes, the VP can cross in 5 minutes and the MD takes 10 minutes to cross. How can they all make it to the meeting in time?

First, the Analyst takes the flashlight and crosses the bridge with the Associate. This takes 2 minutes. The Analyst then returns across the bridge with the flashlight taking 1 more minute (3 minutes passed so far). The Analyst gives the flashlight to the VP and the VP and MD cross together taking 10 minutes (13 minutes passed so far). The VP gives the flashlight to the Associate, who recrosses the bridge taking 2 minutes (15 minutes passed so far). The Analyst and Associate now cross the bridge together taking 2 more minutes. Now, all are across the bridge at the meeting in exactly 17 minutes. Note, that instead of investment bankers, you'll often see the same question using members of musical bands (usually either the Beatles or U2).

You are given 12 balls and a scale. Of the 12 balls, 11 are identical and 1 weighs slightly more. How do you find the heavier ball using the scale only three times?

First, weigh 5 balls against 5 balls (1st Use of Scale). If the scale is equal, then discard those 10 balls and weigh the remaining 2 balls against each other (Second Use of Scale). The heavier ball is the one you are looking for. If on the first weighing (5 vs 5), one group is heavier, then of the heavier group weigh 2 against 2 (2nd Use of Scale). If they are equal, then the 5th ball from the heavier group (the one not weighed) is the one you are looking for. If one of the groups of 2 balls is heaver, then take the heaver group of 2 balls and weigh them against each other (Third Use of Scale). The heavier ball is the one you are looking for.

You own a pet store. If you put in one canary per cage, you have one canary too many. If you put in two canaries per cage, you have one cage too many. How many canaries and cages do you have?

Four canaries and three cages.

You start with a single lily pad sitting on an otherwise empty pond. You are told that the surface area of the lily doubles every day and that it will take 30 days for the single lily to cover the surface of the pond. | If instead of one lily pad you start with eight lily pads (each identical in characteristics to the original lily), how many days will it take for the surface of the pond to be covered? Assume that they don't overlap each other.

If the eight lilies are identical in nature to the single lily then you can think of the eight lily pads as one big lily pad. The question then becomes how many days for one lily to become equivalent to eight lilies. You can subtract this time saved from 30 days. It takes three days for a single lily to grow to the equivalent of eight lilies. So you can shave three days off of 30.

You have 100 balls (50 black balls and 50 white balls) and 2 buckets. How do you divide the balls into the two buckets so as to maximize the probability of selecting a black ball if 1 ball is chosen from 1 of the buckets at random?

Just to be perfectly clear, you are assuming that one of the two buckets is chosen at random and then one of the balls from that bucket is chosen at random. You want to put 1 black ball in 1 of the buckets and all of the other 99 balls in the other bucket. This gives you just slightly less than a 75% change of having a black ball chosen. The math works as follows: There's a 50% chance of selecting the bucket containing 1 ball with a 100% chance of selecting a black ball from that bucket. And a 50% chance of selecting the bucket containing 99 balls with a ~49.5% (49/99) chance of selecting a black ball from that bucket. Total probability of selecting a black ball is (50% % 100%) + (50% * 49.5%) = 74.7%. Posted onJanuary 27, 2010CategoriesInterviewing - Brainteasers A car travels a distance o

You drive to the store at 20 mph and return by the same route at 30 mph. Discounting the time spent at the store, what was your average speed?

Let d be the distance between your home and the store. Then the average velocity for the whole trip would be the total distance divided by the total time. The times for the trips to and from the store would be d/20 mph and d/30 mph, respectively. So, to calculate the velocity: V=d+d / d/20 + d/30 =60 x 2d/ 3d + 2d =120d/5d =24 mph

A car travels a distance of 60 miles at an average speed of 30 mph. How fast would the car have to travel the same 60 mile distance home to average 60 mph over the entire trip?

Most people say 90 mph but this is actually a trick question! The first leg of the trip covers 60 miles at an average speed of 30 mph. So, this means the car traveled for 2 hours (60/30). In order for the car to average 60 mph over 120 miles, it would have to travel for exactly 2 hours (120/60). Since the car has already traveled for 2 hours, it is impossible for it to average 60 mph over the entire trip.

What is unusual about the following words: revive, banana, grammar, voodoo, assess, potato, dresser, uneven?

Place the first letter at the end of the word instead and it'll spell the same word backwards!

You are blindfolded and sit in front of a table. On the table is a large number of coins, 10 of which have heads facing up. How do you split the group of coins into two groups such that the same number of coins are heads-up in each group? Note: You don't know how many coins there are and you can't tell which side is facing up in any way.

Separate 10 of the coins from the group and put them to one side and turn all of the coins in the group of 10 on to their opposite sides.

There's a cabin in the woods and within it, two men lay dead. The cabin did not burn, but the wood around the cabin did. How did the men die?

The 'cabin' is actually a plane cabin and the two men died in a plane crash!

McNuggets come in boxes of 6, 9, and 20. What is the largest number of nuggets that it is not possible to obtain by purchasing some combination of these boxes?

The answer is 43. Solution For any desired number if it is divisible by 3 it can easily be made with 6 and 9 packs, except if the number is 3 itself. If you can't use all six packs then use one 9 pack and you can do the rest with six packs. If the number is not divisible by 3 then use one 20 pack. If the remaining number is divisible by 3 then use the above method for the rest. If the number still isn't divisible by 3 use a second 20 pack. The remainder must be divisible by 3, in which case use the 6 and 9 packs as above. The largest impossible number would be such that you would have to subtract 20 twice to get a remainder divisible by 3. However, you can't make 3 itself with 6 and 9 packs. So the largest impossible number is 2*20+3=43.

Three envelopes are presented in front of you by an interviewer. One contains a job offer, the other two contain rejection letters. You pick one of the envelopes. The interviewer then shows you the contents of one of the other envelopes, which is a rejection letter. The interviewer now gives you the opportunity to switch envelope choices. Should you switch?

The answer is yes. Say your original pick was envelope A. Originally, you had a 1/3 chance that envelope A contained the offer letter. There was a 2/3 chance that the offer letter was either in envelope B or C. If you stick with envelope A, you still have the same 1/3 chance. Now, the interviewer eliminated one of the envelopes (say, envelope B), which contained a rejection letter. So, by switching to envelope C, you now have a 2/3 chance of getting the offer and you've doubled your chances. Note that you will often get this same question but referring to playing cards (as in 3-Card Monte) or doors (as in Monte Hall/Let's Make a Deal) instead of envelopes.

If, having only one match, on a freezing winter day, you entered a room which contained a lamp, a kerosene heater, and a wood burning stove, which should you light first.

The match

You're trying to crack a three-number dial safe. Without knowing the combination numbers, what is the maximum number of trials required to open the safe? A trial is considered a full three-number combination. There are 40 numbers on this safe. To enter a combination you start with the dial at zero and turn counter-clockwise until the first number, then clockwise back to zero, then clockwise to the second number, then counter-clockwise back to zero, and finally counter-clockwise to the third number. Upon the correct combination, the safe will spring open.

The quick answer is generally 40 to the third power, 64,000. This number can be reduced greatly. If you input the first two numbers correctly you don't need the third, you only need to turn the dial through the numbers until the safe springs open. This brings the answer down to 40 to the second power, or 1,600.

A snail is climbing a 10-foot flag pole. He climbs up three feet every 45 minutes. He likes to take naps for 15 minutes after climbing. While sleeping, he slides down by one foot. How long until he reaches the top of the pole?

The quick answer is to establish that the snail climbs a net of 2 feet per hour, reaching the top in 5 hours. Yet, you can't forget about the max height of each hour. The snail's max height is always 1 foot higher than where he slides down to by the end of the hour.

What is the sum of all the numbers from 1 to 100?

The sum of the numbers 1-100 would be equal to the number of pairs (50) multiplied by the sum of each pair (101), or 50 x 101 = 5,050.

You walk across a bridge and you see a boat full of people, yet there isn't a single person on board. How is that possible

The word "single" actually refers to marital status, not the number of people on board. So, the boat is full, but everyone on board is married!

Two planes take off at the same exact moment. They are flying across the Atlantic. One leaves New York and is flying to Paris at 500 miles per hour. The other leaves Paris and is flying to New York at only 450 miles per hour ( because of a strong head wind ). Which one will be closer to Paris when they meet?

They will both be the same distance from Paris when they meet

A man leaves home for a mountain at 1pm and reaches the top at 3pm. The following day he departs from the top at 1pm and gets home at 3pm, by following the same path as the day before. Was he necessarily ever at the same point on the path at the same time on both days?

Yes

There are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes have been incorrectly labeled such that no label identifies the actual contents of the box it labels. Opening just one box, and without looking in the box, you take out one piece of fruit. By looking at the fruit, how can you immediately label all of the boxes correctly? Which box should you choose from?

You know the labels are incorrect so the box labeled "Apples and Oranges" must be either all apples or oranges. Suppose you remove an orange, the box must therefore be all oranges. You now have two labels left: "Apples" & "Apples and Oranges". Also remaining are two incorrectly labeled boxes: "Oranges" & "Apples". Since the "Apples" label can't go on the box already labeled "Apples" you know this one must be "Apples and Oranges". You now have one box and one label so by process of elimination you can correctly label the last box "Apples".

There are three boxes of eggs. In each box is either big eggs, small eggs or big and small eggs. The boxes are labelled "big," "small," and "mixed," but every box mislabeled. What is the least number of boxes you can open to know which eggs are in which box?

You open the box marked BIG and it's filled of the small eggs. You know that the other two boxes must contain the big and mixed egg groups. Those two boxes are marked SMALL and MIXED. Now the box labelled MIXED must hold the big eggs because all boxes are labelled incorrectly. Which leaves the SMALL box holding the big eggs.

What belongs to you, but is mostly used by others?

Your name

You are given 12 balls and a scale. Of the 12 balls, 11 are identical and 1 weighs EITHER slightly more or less. How do you find the ball that is different using the scale only three times AND tell if it is heavier or lighter than the others?

rs? Significantly harder than the last question! Weigh 4 vs 4 (1st Weighing). If they are identical then you know that all of 8 of these are "normal" balls. Take 3 "normal" balls and weigh them against 3 of the unweighed balls (2nd Weighing). If they are identical, then the last ball is "different." Take 1 "normal" ball and weigh against the "different" one (3rd Weighing). Now you know if the "different" ball is heavier or lighter. If, on the 2nd weighing, the scales are unequal then you now know if the "different" ball is heavier (if the 3 non-normal balls were heavier) or lighter (if the 3 non-normal balls were lighter). Take the 3 "non-normal" balls and weigh 1 against the other (3rd Weighing). If they are equal then the third ball not weighed is the "different" one. If they are not equal then either the heavier or lighter ball is "different" depending on if the 3 "non-normal" balls were heavier or lighter in the 2nd Weighing. If, on the 1st Weighing, the balls were not equal then at least you know that the 4 balls not weighed are "normal." Next, take 3 of the "normal balls" and 1 from the heavier group and weigh against the 1 ball from the lighter group plus the 3 balls you just replaced from the heavier group (2nd Weighing). If they are equal then you know that the "different" ball is lighter and is 1 of the 3 not weighed. Of these 3, weigh 1 against 1 (3rd Weighing) If one is lighter, that is the "different" ball, otherwise, the ball not weighed is "different" and lighter. If, on the 2nd weighing from the preceding paragraph, the original heavier group (containing 3 "normal" balls) is still heavier, then either one of the two balls that were NOT replaced are "different." Take the one from the heavier side and weigh against a normal ball (3rd Weighing). If it is heavier, it is "different," and heavier otherwise the ball not weighed is "different" and lighter. If, on the 2nd weighing, the original lighter side is now heavier, then we know that one of the 3 balls we replaced is "different." Weigh one of these against the other (3rd Weighing). If they are equal, the ball not weighed is "different" and heavier. Otherwise, the heavier ball is the "different" one (and is heavier). If you get this right and can answer within the 30 minutes alloted for the interview, then you probably do deserve the job.