Two Identical Units

Draw two lines in the following figure to create two identical units:

 

 

 

Answer:

 

Isobar

Isotherm is to temperature as isobar is to:

 

atmosphere, wind, pressure, latitude, current

 

 

Answer:

pressure

Odd One Out

Which number is the odd one out?

9678  4572  5261  5133  3527  6895  7768

Answer:

3527: in the others the sum of the first two numbers is equal to the sum of the second two numbers, for example 5 + 2 = 6 + 1.

0, 1, 2, 4, 6, 9, 12, 16, ?

0, 1, 2, 4, 6, 9, 12, 16, ?

What number should replace the question mark?

Answer:

20: add 1, 1, 2, 2, 3, 3, 4, 4.

Most Opposite

Which word in brackets is most opposite to the word in capitals?

PROSCRIBE (allow, stifle, promote, verify, indict)

Answer:

allow

Form a Perfect Square

Which piece below, when fitted into the piece on the left, will form a perfect square?

 

 

Answer:

B

True and False Statements

Which of the following statements are true and which are false?

 

Answer:

A is true; B is false (the majority are concave); C is false (a spider has eight legs); D is false

(a stalagmite grows upwards, whereas as stalactite grows downwards).

Which row is the odd one out?

Which row is the odd one out?

Which row is the odd one out?

Answer:

D

Apart from D, each row contains one figure with one stroke, one with two strokes, one with three strokes, one with four strokes and one with five strokes. In row D there are two figures with four strokes and none with five strokes.

4,4,3,3,2,2,1

Create a number using only the digits 4,4,3,3,2,2,1 and 1. So it can only be eight digits. You have to make sure the ones are separated by one digit, the twos are separated by two digits the threes are separated with three digits and the fours are separated by four digits.


 

Answer:

41312432

How many lockers are open?

A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?
 

Answer:

The only lockers that remain open are perfect squares (1, 4, 9, 16, etc) because they are the only numbers divisible by an odd number of whole numbers; every factor other than the number's square root is paired up with another. Thus, these lockers will be 'changed' an odd number of times, which means they will be left open. All the other numbers are divisible by an even number of factors and will consequently end up closed. So the number of open lockers is the number of perfect squares less than or equal to one thousand. These numbers are one squared, two squared, three squared, four squared, and so on, up to thirty one squared. (Thirty two squared is greater than one thousand, and therefore out of range.) So the answer is thirty one.

Find out a multi-digit number!

Try to find out a multi-digit number that if multiplied by the number 9 or any of its multiplications products (18, 27, 36, 45,..) will result in the multiplication factor repeated (n) number of times.


 

Answer:

The number is: 12345679
12345679 * 9 = 111111111
12345679 * 18 = 222222222
12345679 * 27 = 333333333
And so on ...

What should Henry choose?

Henry has been caught stealing cattle, and is brought into town for justice. The judge is his ex-wife Gretchen, who wants to show him some sympathy, but the law clearly calls for two shots to be taken at Henry from close range. To make things a little better for Henry, Gretchen tells him she will place two bullets into a six-chambered revolver in successive order. She will spin the chamber, close it, and take one shot. If Henry is still alive, she will then either take another shot, or spin the chamber again before shooting.

Henry is a bit incredulous that his own ex-wife would carry out the punishment, and a bit sad that she was always such a rule follower. He steels himself as Gretchen loads the chambers, spins the revolver, and pulls the trigger. Whew! It was blank. Then Gretchen asks, 'Do you want me to pull the trigger again, or should I spin the chamber a second time before pulling the trigger?'

What should Henry choose?
 

Answer:

Henry should have Gretchen pull the trigger again without spinning.

We know that the first chamber Gretchen fired was one of the four empty chambers. Since the bullets were placed in consecutive order, one of the empty chambers is followed by a bullet, and the other three empty chambers are followed by another empty chamber. So if Henry has Gretchen pull the trigger again, the probability that a bullet will be fired is 1/4.

If Gretchen spins the chamber again, the probability that she shoots Henry would be 2/6, or 1/3, since there are two possible bullets that would be in firing position out of the six possible chambers that would be in position.