#11 - Ant Problem Probability Quiz

Three ants are sitting at the three corners of an equilateral triangle. Each ant starts randomly picks a direction and starts to move along the edge of the triangle. What is the probability that none of the ants collide?

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So let’s think this through. The ants can only avoid a collision if they all decide to move in the same direction (either clockwise or anti-clockwise). If the ants do not pick the same direction, there will definitely be a collision. Each ant has the option to either move clockwise or anti-clockwise. There is a one in two chance that an ant decides to pick a particular direction. Using simple probability calculations, we can determine the probability of no collision.

#12 - IQ PUZZLE

You have two strings whose only known property is that when you light one end of either string it takes exactly one hour to burn. The rate at which the strings will burn is completely random and each string is different.

How do you measure 45 minutes?

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Light both the ends of the first string and one end of the second string. 30 minutes will have passed when the first string is fully burned, which means 30 minutes have burned off the second string. Light the end of the second string and when it is fully burned, 45 minutes will have passed.

#13 - Monday Cipher Puzzle

Can you decipher the following common phrase?

T M C
A U O
H S M
W T E

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What goes up must come down.

#14 - Math Teaser

Find three whole, positive numbers that have the same answer when multiplied together as when added together.

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1,2, & 3

1 x 2 x 3 = 6 and 1 + 2 + 3 = 6

#15 - Missing Number in this Sequence

Can you discover the missing number in this series?

37, 10, 82
29, 11, 47
96, 15, 87
42, ?, 15

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The missing number is 6.
The number in the middle of each triple is the same as the digits of either end's number when added together. 3+7=10=8+2 and so on.

#16 - 4 Doors Riddle

You are an expert on paranormal activity and have been hired to locate a spirit haunting an old resort hotel. Strong signs indicate that the spirit lies behind one of four doors. The inscriptions on each door read as follows:

Door A: Its behind B or C
Door B: Its behind A or D
Door C: Its in here
Door D: Its not in here

Your psychic powers have told you three of the inscriptions are false, and one is true. Behind which door will you find the spirit?

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The spirit lies behind Door D.

If the spirit is behind Door A, then both B and D are true.

If the spirit is behind Door B, then both A and D are true.

If the spirit is behind Door C, then A, C, and D are all true.

If the spirit is behind Door D, then the statements on all the doors are false, except for that on Door B. This matches the rules, and therefore, the resort hotel spirit lurks behind Door D.

#17 - Short Easy Riddle

A boy was at a carnival and went to a booth where a man said to the boy, 'If I write your exact weight on this piece of paper then you have to give me $50, but if I cannot, I will pay you $50.' The boy looked around and saw no scale so he agrees, thinking no matter what the carny writes he'll just say he weighs more or less. In the end the boy ended up paying the man $50. How did the man win the bet?

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The man did exactly as he said he would and wrote 'your exact weight' on the paper.

#18 - CAT Exam Puzzle

5+3+2 = 151022
9+2+4 = 183652
8+6+3 = 482466
5+4+5 = 202541
THEN ;
7+2+5 =

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7*2 , 7*5 , 7*2 + 7*5 -2

#19 - Interesting Number puzzle

A number with an interesting property:

When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.

It's not a small number, but it's not really big, either.
When I looked for a smaller number with this property I couldn't find one.

Can you find it?

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The number has to end in 9.
Looked brute force for small numbers.
59 and 119 were promising, but no cigar.

Then looked for agreement among
39 + multiples of 40,
69 + multiples of 70 and
89 + multiples of 90
Smallest one was 2519.

#20 - Distance Puzzle

Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 18 MPH between the 2 friends until the friends meet.

How many miles does the pigeon travel?

View Answer Discuss

54
It takes 3 hours for the friends to meet; so the pigeon flies for 3 hours at 18 MPH = 54 miles