Here in South Louisiana we seem to have a envie (ahnvee) for telling jokes, or in some cases asking tricky questions. I read a recent article outlining some great brainteasers for engineers.
The following are in no particular order and include examples from tech company interviews and classic riddles. There are many, many more out there as you can appreciate. Enjoy!
1. mardi gras doubloon Toss (Coin Toss)
Brainteaser: You toss two doubloons. If you get heads with the first, you stop. If you get tails, you toss it again. The second doubloon is tossed regardless. What is the ratio of heads to tails?
Answer: 1 to 1
Workings: You would expect the odds of heads or tails to be 50/50 for any tossed doubloon. You would then expect to toss the first doubloon at least twice. This should, by rights, give you a ratio of 1 to 1.
The second doubloon is continuously tossed and it should also have a ratio of 1 to 1. Hence the ratio of the two must, therefore, also be 1 to 1.
2. Plant your T-post
Brainteaser: If you have a square room with no roof, and you had four t-posts you had to plant on the walls so that each t-post touched two walls, how would you do it?
Answer: Put them in corners dummy
Workings: Yup, you probably got this one off the bat. Plant them in the corners and by virtue, they are touching two walls each.
3. Weighing things up: Boudin Ball Style
Brainteaser: Given 9 boudin balls all of which weigh the same except for one, what is the minimum of weighings necessary to find the ball that weighs more (or less)?
Workings: Theoretically you should be able to do this in two weighings, so long as its a two pan balance. Firstly, take two pairs of three balls and weigh them first. If they balance, you know the “odd” ball is in the last three balls.
From that group take two balls and weigh them against each other. Again if they balance its the last one remaining.
If however, the first six balls don’t balance grab the set that is lighter or heavier (depending on criteria). In this case, repeat the second step above.
4. Throw it overboard
Brainteaser: You’re in a pirogue and you throw out a sack of decoys. Does the water level increase?
Workings: Water is already being displaced, if you like, by its contributing weight and density to the submerged part of the pirogue’s hull.
So by throwing it overboard, its weight/density will not alter things. If it’s denser than water it will sink and displace its total volume, and if it’s lighter it will displace the portion of its volume dictated by its weight/density. In either case, there will be no change compared to its existing effect.
5. Burning Crab Lines
Brainteaser: You have 2 pieces of crab line, 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 crab line properties that were not stated. Given only 1 match, can you time 45 minutes?
Answer: Place one of the crab lines at the midpoint between the other and light. Either one line in a circle or forming a T.
Workings: Depending on the accuracy you are after either solution will work. You could form the first crab line into a circle with both ends touching.
Then place the other line, straight, more or less, 180 degrees directly opposite the touching ends.
Then light the circular crab line touching ends.
You could alternatively form a T with one of the lines bisecting the other at its exact midpoint and light the end of the “vertical” line, or indeed simultaneously light both ends of the “horizontal” one. In both cases, you get 30 minutes/2 for the circular crab line or “horizontal” line plus 30 minutes for the other line to give you a total of 45 minutes.
6. Which switch?
Want some more brainteasers for engineers, here’s a fun one.
Brainteaser: In front of you are three light switches. Only one does anything, and it turns on the light in the mud boat shed.
From here you can’t see the light, and it makes no sound.
You must determine which switch operates the light, BUT you can only go check it once. How do you figure out which switch is for the light?
Answer: 2 switch flicks and a portion of time you can’t get back 🙂
Workings: Light bulbs convert electricity into light and heat right? So, it doesn’t matter which switches you turn on or what order.
Try one and wait 5-10 minutes. This should be enough time to make them “hot” if correct. 5-10 minutes should be enough time. If it’s not that one the light will be off and cold right?.
Flick the second one, it doesn’t matter which so long as it’s not the first one. Again wait another 5-10 minutes. Ok, we are assuming the bulb doesn’t lose all of its “heat” within this time limit.
Now go and check. If the light is on, great you know it’s the second one. It could be off and hot, in this case, it is the first one. If it’s off and cold (assuming it won’t lose its “heat” in the time that’s passed) it’s the last un-flicked one. Or you could trace the wiring, whatever.
7. Pig Trap problems
Brainteaser: The probability of finding the pig trap occupied is 1/3. You find it empty for 9 consecutive days. Find the probability that it will be empty on the 10th day.
Workings: At first this may seem to be a trick question. With probability, you would be forgiven for thinking this, but often it’s not. The fact it’s been empty for 9 consecutive days doesn’t influence the probability of it’s “condition” on the 10th day.
8. Losing your Hunting Tags
Brainteaser: Imagine that you have three hunting bags, one containing two deer tags, one containing two turkey tags, and the third, one deer tag and one turkey tag.
The bags were labeled for their contents – DD, TT, DT – but someone has switched the labels so that every bag is now incorrectly labeled.
You are allowed to take one tag at a time out of any bag, without looking inside, and by this process of sampling, you are to determine the contents of all three bags. What is the smallest number of drawings needed to do this?
Workings: Read the question again carefully. The main thing to remember is that the bags are incorrectly labeled.
You can then guarantee the contents of each bag with one draw. Let’s say you draw a tag from the bag labeled DT. You know this is wrong initially, thus it can only by DD or TT, right? If you draw a turkey tag you know this bag must be TT.
That leaves two more unknown bags. The bag labeled DD cannot be DD as the labels are wrong. This must, therefore, be DT.
Continue with this logic and you can ascertain the correct label for the last one.
9. Crawfish Farmer challenge
Brainteaser: A crawfish farmer challenges an engineer, a physicist, and a mathematician to levee off the largest amount of area using the least amount of dirt.
The engineer made his levee in a circle and said it was the most efficient. The physicist made a long line and said that the length was infinite.
Then he said that creating a levee around half of the earth was the best. The mathematician laughed at the others and with his design, beat the others. What did he do?
Answer: The mathematician tricks the other two. How?
Workings: As we know the engineer built a nice circular levee and claimed it was efficient. The physicist decided to make a long line levee of infinite length. He claimed that half the earth should have a levee for best results. Ok so what about the mathematician? We’ll this educated cajun decided to build a levee around himself. He then claimed he was on the outside of the levee. Nice.
10. GUlp Bait, Gulp bait everywhere!
Brainteaser: There are 20 different gulp bait packs of two types, glow and chartreuse, in a tackle box in a completely dark room. What is the minimum number of packs you should grab to ensure you have a matching pair?
Workings: The suggested answer given here is more to show an appreciation of the real world rather than theory, statistics etc. With this in mind, the only way to safely “ensure you have a matching pair” is to pick 11 packs. They say that this is the only foolproof “guaranteed” method of getting a pair in the real world.
So there you go, a selection of some interview brainteasers for engineers and classic riddles. Could you answer them all? Good for you. Do you have any favorites you’d like to share? Send them to us here.