interview questions engineers struggle to answer

Q: How many trailing zeros are in the number 5! (5 factorial)?

Asked to: Systems engineer at Google

Suggested answers:

Option 1: 5!=120. So there is 1 trailing zero.

Option 2: This sounds like one geared not so much towards getting the right answer, but getting to it the right way. If you think a bit and say "one", the interviewer will know you did it the brute-force way, doing the math. You'd get at the answer faster, and probably impress them more, if you think instead how many times a ten will be produced in doing that math, rather than what the actual result of the math will be.

Q: You have two light bulbs at a 100-story building. You want to find the floor at which the bulbs will break when dropped. Find the floor using the least number of drops.

Asked to: Software engineer at Facebook

Suggested answers:

Option 1: Start moving up in increments of 10 floors and dropping the bulb until it breaks (ie: drop from floor 10, if it doesn't break, drop from floor 20, etc.) Once the bulb breaks, move down to the floor before it broke on and start moving up floors in increments of one until the second bulb breaks. This results in a worst case scenario of 19 drops.

Option 2: 19 drops is not the best worst-case scenario... imagine trying floor 16, if it breaks, you try 1 - 15 and thats 16 tries. If it doesn't break, then try floor 31 and if it breaks, then try 17 - 30 (so 16 tries, including the try on floor 16). And on and on (45, 58, 70, 81, 91, 100). If you reach 91, you'll have tried 7 floors so far and if it doesn't break, then there's 9 more tries to get to 100 (thus 16 in the worst case.)

Q: If you had 5,623 participants in a tournament, how many games would need to be played to determine the winner?

Asked to: Manager at Amazon

Suggested answers:

Option 1: The interviewer is not looking for the right answer because there can be many. What he/she is looking for is your logical approach in solving the answer. So you could start by probing more is first I would like to understand if 5,623 participants represent the number of team or individuals. Then ask the next logical question based on the answer."

Option 2: 5,622. Assuming it is a single elimination tournament. All teams lose one game except the champs. It's always # of teams - 1.

Q: There are 20 different socks of two types in a drawer in a completely dark room. What is the minimum number of socks you should grab to ensure you have a matching pair?

Asked to: Software development engineer in test at Web trends

Suggested answer: I'm not a mathematician, statistician, or highly analytical but if you pick up three socks they could still be all of same type -- even if the odds are 50%. Odds do not equal reality. So the only way to 'ensure you have a matching pair' is to pick up 11 of the 20. This is the only foolproof guaranteed way to get a pair (in the real world and not the world of odds.)

Q: If you have a square room with no roof, and you had four flagpoles you had to plant on the walls so that each flagpole touched two walls, how would you do it?

Asked to: Software engineer at Cisco

Suggested answer: The answer was that by planting them on the corners, each one is touching two walls because each corner is part of two walls. I wanted to pierce two walls with a pole horizontally too. They said it was an innovative solution.

Q: There are 9 balls all of which weigh the same except one, what is the minimum weighings necessary to find the ball weighs more (or less)?

Asked to: Software engineer at DE Shaw & Co

Suggested answer: You could do this with two weighings assuming its a two pan balance -- (1) place three balls on each side if they balance out then its the remaining three that has abnormal ball (2) out of that group, place one ball on each side -- if balances it out, the abnormal ball is the remaining one. If the weighing in step (1) does not balance out, grab the group of three balls that is light or heavy and repeat step (2) described above."

Q: You have 2 pieces of rope, each of which burns from one end to the other in 30 minutes (no matter which end is lit). If different pieces touch, the flame will transfer from one to the other. You cannot assume any rope properties that were not stated. Given only 1 match, can you time 45 minutes?

Asked to: ASIC verification engineer at Zoran

Suggested answers:

Option 1: Take one rope (Rope A), place it down as a circle. Light match and start burning rope A at the tips that are touching. When the rope completely burns out, 15 minutes will have passed (since both ends are burning and being consumed at once). Hold the second rope (Rope B) straight and place one end so that it will immediately catch fire when the two burning points from (Rope A) finally touch and are just about to burn out. Thus 15 minutes on Rope A + 30 minutes on Rope B gives you 45 mins.

Option 2: Make a T simple.