Brain teasers are often used by major tech companies, like Intel, Google and Yahoo, to test prospective employees on how sharp their thinking is.
Here are some of the very best "Problems of the Week"; many of which I’ve used for years to challenge my GATE fifth graders. However, there is no set grade level or age group for such problems; they will challenge anyone, all the way up to highly educated adults. But, I will often get ingenious or near-automatic responses from kids as young as 10, whose razor-sharp thinking brought the solution immediately to mind. Others will work carefully and methodically all week, and either finally arrive at the solution in a true “Aha!” moment, or eventually throw up their hands. I will also often get frantic emails from parents, many of whom are doctors, lawyers, engineers, and the like, begging for hints. On the other hand, as I said, kids will occasionally solve these on the spot; you never can tell.
Note: I have culled these from a wide variety of sources. Most of these are considered “classics,” and can be found all over in various versions. Few, if any, could be considered original. I’ve found multiple variations of these in various books, on web sites; everywhere. The ones I’ve selected for you, though, I consider to be the most intriguing, engaging, and in some cases, downright diabolical. Have fun with these, and resist the temptation to peek at the answers right away. The thrill of arriving at a successful solution is a very heady feeling you don’t want to miss.
Brain Teaser Questions
1. There are four girls. In front of them is a basket containing four apples. Every girl takes an apple yet at the end, one apple remains in the basket. How can this be?
2. A man says, "Brothers and sisters, have I none, but that man's father is my father's son." Who is he pointing at?
3. Janice and Marge were roommates in college, and meet again after many years. What are the ages of each of the children? Here is their discussion:
Janice: I have three children.
Marge: What are their ages?
Janice: Well, the product of their ages is 36.
Marge: I need more information.
Janice: The sum of their ages is our old dorm room number.
Marge: That’s still not enough information.
Janice: The oldest one is a girl.
Marge: Now I know their ages!
4. You have a 1-minute string fuse and it burns unevenly: fast then slow, slow then fast, etc. You have one match, no clocks, and no other timing devices. How do you time exactly 30 seconds?
5. There are three boxes; one contains only apples, one contains only oranges, and one contains both apples and oranges. However, every one of the boxes has been incorrectly labeled; no label identifies the actual contents of the box. Opening just one box, and without looking in the box, you take out one piece of fruit. By looking at the fruit, you can immediately label all of the boxes correctly. Which box did you open?
6. A boy and a girl are sitting on the porch. "I'm a boy," says the child with black hair. "I'm a girl," says the child with red hair. If at least one of them is lying, who is which?
7. A windowless room contains three identical light fixtures, each containing an identical light bulb. Each light is connected to one of three switches outside of the room. Each bulb is switched off at present. You are outside the room, and the door is closed. You have one, and only one, opportunity to flip any or all of the external switches as much as you like. After this, you can go into the room and look at the lights, but you may not touch the switches again. How can you tell which switch goes to which light?
8. A bouncer and a patron were arguing so loudly in a nightclub that the Police Dept. had to be called. “Officer, it’s no big deal, ok?” said the patron. “The bouncer is my brother anyway.” But when questioned, the bouncer told police “I don’t have a brother.” Both are telling the truth; how can this be?
9. The weather during Caroline’s vacation was strange. It rained on 15 different days, but it never rained for a whole day. How long was Caroline’s vacation?
- Rainy mornings were followed by clear afternoons.
- Rainy afternoons were preceded by clear mornings.
- There were 12 clear mornings and 13 clear afternoons in all.
10. A drink machine offers three selections - Tea, Coffee or Random, but the machine has been incorrectly wired so that each button does NOT give what it claims. If each drink costs $.50, what is the minimum amount of money you will have to put into the machine to determine which button gives which selection?
11. You have a 10-gallon jug and a 3-gallon jug. Neither jug is labeled. You need exactly 5 gallons of water. You have a working water faucet right next to you. How can you get exactly 5 gallons of water?
12. You are in the dark, and on the floor there are six shoes of three colors, and a heap of twenty-four socks, which are either black or brown. How many socks and shoes must you take into the light to be certain that you have a matching pair of socks and a matching pair of shoes?
13. There are 12 gold coins. All of them are fake except for one. All of them appear exactly the same, and there is no way to tell them apart. However, there is one difference: the real gold coin is slightly heavier than the others. Using a balance scale, how can you determine which is the fake coin, with only three weighings?
Brain Teaser Answers
1. The last girl takes the apple along with the basket.
2. He must be the son of the father since he has no brothers, so he is pointing at his son.
3. 2, 2 and 9. From the products, you get 1,1,36 1,2,18 1,3,12 1,4,9 1,6,6 2,2,9 2,3,6 3,3,4. Since the sum equals the dorm room number, you can eliminate all but two possibilities, because all the other sums are unique and you would have an obvious answer. For instance, if their room number were 16, the ages would have to be 1, 3, and 12. The two possibilities remaining would be 1, 6, and 6, and 2, and 9. But once you know that the oldest one is a girl, you can eliminate 1, 6, and 6 because the oldest two have the same age; thus there is no oldest son. That leaves the only remaining possibility as 2, 2, and 9.
4. Burn the fuse at both ends!
5. You must open the box labeled “apples and oranges." Remember, by definition, whichever fruit is inside, that will be the only type of fruit in that particular box. So let's say that you found an apple in that box labeled “apples and oranges;” because you know it must therefore only contain apples, you can also conclude that the box labeled as "oranges" cannot contain only oranges, since you know that all the boxes are supposedly mislabeled. Thus, the box labeled "oranges" must contain both apples and oranges, leaving the box labeled "apples" to contain only oranges.
6. If there is one child of each gender on the bench, and, at least one is lying, then both must be lying. If only one was lying, that would mean that were would have to be two children of the same sex. Since in that case it would violate the given rules, it must be that each child is of the opposite sex from what each says they are.
7. There are various ways, most of them fairly similar. One is to turn one on for a while, then shut it off. Then turn another on for just a few seconds. Then when you go into the room, feel the bulbs. The hot one is the first one, the lukewarm one the second, etc.
8. No one’s lying. It’s his sister.
9. You take half of 12+13+15, so 20. Why? A and B together tell you that each of the 15 rainy days included either a clear morning or a clear afternoon, but not both of course. So the total of rainy mornings or afternoons is 15. The total of clear mornings or afternoons is 12+13=25. So the total of mornings or afternoons is 15+25=40, which is twice the number of days.
10. There are different ways to work through this, but here is one way: start with the “Random” button. Of course, we know this is NOT Random, so if it dispenses Tea it is the Tea button; likewise, if it dispenses Coffee it is the Coffee button. From this point, it is simple to work out the other buttons, because you know that they can't be what they say they are. At the end, you’ll be left with only two possible combinations, which means it will only cost $.50 to figure out which is which.
11. This is a little involved!
- Fill the 3 gallon jug four times, each time dumping the water from it into the 10 gallon jug.
- After you do this for the fourth time, this will leave two gallons of water in the 3 gallon jug, and the 10 gallon jug will be filled.
- Dump out the water from the 10 gallon jug.
- Empty the two gallons from the 3 gallon jug into the 10 gallon jug.
- Now fill the 3 gallon jug again, and dump the water into the 10 gallon jug. This leaves 5 gallons of water in the 10 gallon jug.
12. Three socks and four shoes would guarantee that you would have a matching pair of each. Since there are only two colors of socks, it doesn't matter how many are in the heap, as long as you take at least three, you are certain to have two of the same. As for the shoes, you must pick four, because selecting only three could result in one shoe in each of the three colors!
13. First, weigh all 12 gold coins, 6 on each side of the scale (weighing #1). Whichever side is heavier, take those 6 gold coins and weigh 3 on each side (weighing #2). Again, whichever side is heavier, take those 3 gold coins, placing 1 to the side, and weighing the other 2, one on each side of the scale (weighing #3). During this weighing, if one gold coin weighs heavier than the other, the answer is obvious, and so too, if they balance perfectly, then the gold coin you put to the side is the heavier gold coin!
Improving Deductive Reasoning Skills
This is a great article on how to teach Deductive Reasoning Skills, intended for grades 7-12. It is done through cooperative groupings and solid preparatory work in various approaches and strategies.
This is an intriguing logic puzzle based on a passage from the first Harry Potter novel. It is intended for grades 8-12, and is sure to provide interest and engagement.
This is something a little different: a classic geometric puzzle which is not inherently very difficult to solve, but for which mathematicians strugged for centuries to prove. It is an intriguing puzzle which is intended for a wide range: grades 3-7, and includes interesting follow-up possibilities as well.
Forensics: Get A Clue!
This activity is sure to be a winner with grades 6-8. Learners use a variety of reasoning strategies to solve a classroom "crime. "