Brain Teasers

Question 1

What is the expected value of a roll of a dice?

Answer 1

This is basic probability and the correct answer is 3.5

Question 2

If you look at a clock and the time is 3:15, what is the angle between the hour and the minute hands?

Answer 2

The answer to this is not zero! The hour hand, remember, moves as well.

The hour hand moves a quarter of the way between three and four, so it moves a quarter of a twelfth (1/48) of 360 degrees. So the answer is seven and a half degrees, to be exact.

Question 3

You have a five-gallon jug and a three-gallon jug. You must obtain exactly four gallons of water.
How will you do it?

Answer 3

You should find this brainteaser fairly simple. If you were to think out loud, you might begin by examining the ways in which combinations of five and three can come up to be four. For example: (5 - 3) + (5 - 3) = 4.

This path does not actually lead to the right answer, but it is a fruitful way to begin thinking about the question.

Here’s the solution:
1. Fill the three-gallon jug with water and pour it into the five-gallon jug.

2. Repeat. Because you can only put two more gallons into the five-gallon jug, one gallon will be left over in the three- gallon jug.
3. Empty out the five-gallon jug and pour in the one gallon. Now just fill the three-gallon jug again and pour it into the five gallon jug.

(Mathematically, this can be represented 3 + 3 - 5 + 3 = 4)

Question 4

A company has 10 machines that produce gold coins. One of the machines is producing coins that are a gram lighter. How do you tell which machine is making the defective coins with only one weighing?

Answer 4

Think this through—clearly, every machine will have to produce a sample coin or coins, and you must weigh all these coins together. How can you somehow indicate which coins came from which machine?

The best way to do it is to have every machine crank a different number of coins, so that machine 1 will make one coin, machine 2 will make two coins, and so on.

Take all the coins, weigh them together, and consider their weight against the total theoretical weight. If you’re four grams short, for example, you’ll know that machine 4 is defective.

Question 5

What is the sum of the numbers from one to 50?

Answer 5

Easy question and fairly popular.

Pair up the numbers into groups of 51 (1 + 50 = 51; 2 + 49 = 51; etc.).

Twenty five pairs of 51 equal 1275

Question 6

If you have seven white socks and nine black socks in a drawer, how many do you have to pull out blindly in order to ensure that you have a matching pair?

Answer 6

Three. Let’s see—if the first one is one colour, and the second one is the other colour, the third one, no
matter what the colour, will make a matching pair. Sometimes you’re not supposed to think that hard

Question 7

You are given nine balls, one of which weighs less than the rest. You are also given a traditional two-sided scale.

How many times do you need to weigh balls to determine which is the lightest one?

Answer 7

Like the earlier weighing question, this one will challenge your process of elimination skills.

Most people immediately think three times, but the answer is actually two.

First, you would put six balls on the scale— three
on each side. If the light one is in one of these two groups, you’d know. If not, you know it’s in the final group.

Whatever the case, you weigh two balls (one on each side) from this lighter grouping. If they are equal, the light ball is the odd one out. If they aren’t, you already know the answer.

Question 8

Picture a 10 x 10 x 10 “macro-cube” floating in mid-air. The macro-cube is composed of 1 x 1 x 1 “micro-cubes,” all glued together. The outermost layer falls to the ground. How many micro-cubes are on the ground?

Answer 8

The answer is 488.

The best way to get to the correct answer is to think of the cube that will remain after the outermost layer falls.

The remaining cube will have 8 micro cubes on each side. The number of micro cubes in the remaining macro cube is then 512 (888).

So the number of micro cubes on the ground will be 1,000-512=488.

Question 9

Give me the decimal equivalent of 13/16 and of 9/16?

Answer 9

First you should know how much 1/16 is. You should know this by heart (because this is how US treasuries are still quoted) and the answer is 0.0625.

Now, 13/16 is 1/16 + 3/4. So, it’s 0.0625 plus 0.75. Hence, the answer is 0.8125.

Applying the same reasoning, 9/16 is really 1/2 plus 1/16. Thus, the answer would be 0.5625

Question 10

You hire a man to work in your yard for seven days. You wish to pay him in gold. You have one gold bar with seven parts-like a chocolate bar . You wish to pay him one gold part per day, but you may snap the bar in only two places. Where do you snap the bar so that you may pay him at the end of each day, and so that on successive days he may use what you paid him previously to make change?

Answer 10

1. Snap the bar into pieces that are one, two, and four parts long, respectively.
2. On day one, give him one part.
3. On day two, exchange your two parts for his one.
4. On day three, give him back the one part.
5. On day four, exchange four parts for his three.
6. On day five, give him one more part.
7. On day six, exchange your two parts for his one.
8. On day seven, give him back the one part.