The Miracle Mountain Riddle
A hiker climbs all day up a steep mountain path and arrives at the mountain top where he camps overnight. The next day he begins the descent down the same trail to the bottom of the mountain when suddenly he looks at his watch and exclaims, "That is amazing! I was at this very same spot at exactly the same time of day yesterday on my way up."
What is the probability that a hiker will be at exactly the same spot on the mountain at the same time of day on his return trip, as he was on the previous day's hike up the mountain?
Is the probability closest to (A) 99% or (B) 50% or (C) 0.1% ?
What is the probability that a hiker will be at exactly the same spot on the mountain at the same time of day on his return trip, as he was on the previous day's hike up the mountain?
Is the probability closest to (A) 99% or (B) 50% or (C) 0.1% ?
Hint: This is not a trick. His watch works perfectly well. He does not sit in the same spot all day or any other such device, although it would not change the answer if he did!
The answer is (A). Since it must happen, the probability is actually 1 (100%).
Explanation: Firstly, consider 2 men, one starting from the top of the mountain and hiking down while the other starts at the bottom and hikes up. At some time in the day, they will cross over. In other words they will be at the same place at the same time of day.
Now consider our man who has walked up on one day and begins the descent the next day. Imagine there is someone (a second person) shadowing his exact movements from the day before. When he meets his shadower (it must happen) it will be the exact place that he was the day before, and of course they are both at this spot at the same time.
Contrary to our common sense, which seems to say that this is an extremely unlikely event, it is a certainty.
NOTE: There is one unlikely event here, and that is that he will notice the time when he is at the correct location on both days, but that was not what the question asked. Did you answer this riddle correctly?
YES NO
Explanation: Firstly, consider 2 men, one starting from the top of the mountain and hiking down while the other starts at the bottom and hikes up. At some time in the day, they will cross over. In other words they will be at the same place at the same time of day.
Now consider our man who has walked up on one day and begins the descent the next day. Imagine there is someone (a second person) shadowing his exact movements from the day before. When he meets his shadower (it must happen) it will be the exact place that he was the day before, and of course they are both at this spot at the same time.
Contrary to our common sense, which seems to say that this is an extremely unlikely event, it is a certainty.
NOTE: There is one unlikely event here, and that is that he will notice the time when he is at the correct location on both days, but that was not what the question asked. Did you answer this riddle correctly?
YES NO
Little Billy's Calculator
Little Billy has a calculator with 15 buttons. He has 10 keys for 0-9, a key for addition, multiplication, division, and subtraction. Finally, he has an = sign. However, Mark the Meanie messed up the programming on Billy's calculator. Now, whenever Billy presses any of the number keys, it comes up with a random single-digit number. The same goes for the four operations keys (+,-,x, /). So whenever Billy tries to press the + button, the calculator chooses randomly between addition, multiplication, subtraction, and division. The only key left untouched was the = sign.
Now, if Billy were to press one number key, one operation key, then another number key, then the = button, what are the chances the answer comes out to 6?
Now, if Billy were to press one number key, one operation key, then another number key, then the = button, what are the chances the answer comes out to 6?
Hint: Think about how many ways he could possibly get 6.
There is a 4% chance.
There are 16 possible ways to get 6.
0+6
1+5
2+4
3+3
6+0
5+1
4+2
9-3
8-2
7-1
6-0
1x6
2x3
6x1
3x2
6/1
There are 400 possible button combinations.
When Billy presses any number key, there are 10 possibilities; when he presses any operation key, there are 4 possibilities.
10(1st#)x4(Operation)x10(2nd#)=400
16 working combinations/400 possible combinations= .04 or 4% Did you answer this riddle correctly?
YES NO
There are 16 possible ways to get 6.
0+6
1+5
2+4
3+3
6+0
5+1
4+2
9-3
8-2
7-1
6-0
1x6
2x3
6x1
3x2
6/1
There are 400 possible button combinations.
When Billy presses any number key, there are 10 possibilities; when he presses any operation key, there are 4 possibilities.
10(1st#)x4(Operation)x10(2nd#)=400
16 working combinations/400 possible combinations= .04 or 4% Did you answer this riddle correctly?
YES NO
The Secret Santa Exchange
A group of ten friends decide to exchange gifts as secret Santas. Each person writes his or her name on a piece of paper and puts it in a hat. Then each person randomly draws a name from the hat to determine who has him as his or her secret Santa. The secret Santa then makes a gift for the person whose name he drew.
When it's time to exchange presents, each person walks over to the person he made the gift for and holds his or her left hand in his right hand.
What is the probability that the 10 friends holding hands form a single continuous circle?
When it's time to exchange presents, each person walks over to the person he made the gift for and holds his or her left hand in his right hand.
What is the probability that the 10 friends holding hands form a single continuous circle?
Hint: It's not as difficult as it seems.
It's the number of ways the friends can form a circle divided by the number of ways the names can be drawn out of the hat.
1/10
For a group of n friends, there are n! (n factorial) ways to draw the names out of the hat. Since a circle does not have a beginning and end, choose one person as the beginning and end of the circle. There are now (n-1)! ways to distribute the remaining people around the circle. Thus the probability of forming a single circle is
(n-1)! / n!
Since n! = (n-1)! * n (for n > 1), this can be rewritten as
(n-1)! / (n*(n-1)!)
Factoring out the (n-1)! from the numerator and denominator leaves
1/n
as the probability. Did you answer this riddle correctly?
YES NO
For a group of n friends, there are n! (n factorial) ways to draw the names out of the hat. Since a circle does not have a beginning and end, choose one person as the beginning and end of the circle. There are now (n-1)! ways to distribute the remaining people around the circle. Thus the probability of forming a single circle is
(n-1)! / n!
Since n! = (n-1)! * n (for n > 1), this can be rewritten as
(n-1)! / (n*(n-1)!)
Factoring out the (n-1)! from the numerator and denominator leaves
1/n
as the probability. Did you answer this riddle correctly?
YES NO
An Electric Train Riddle
An electric train is moving north at 100mph and a wind is blowing to the west at 10mph. Which way does the smoke blow?
Hint:
Over London Bridge
As I went over London Bridge
I met my sister Jenny
I broke her neck and drank her blood
And left her standing empty
Who is Jenny?
I met my sister Jenny
I broke her neck and drank her blood
And left her standing empty
Who is Jenny?
Hint:
Two Identical Soldiers
There are two identical soldiers each one is exactly the same. One however is a traitor. So one goes into a tank and the other goes on foot. The traitor succeeds in killing the army. Which one is the traitor?
Hint:
The one that went on foot is because it takes more than one soldier to operate a tank. Did you answer this riddle correctly?
YES NO
YES NO
A Sharpshooter Riddle
A sharpshooter hangs up his hat, turns around and walks 5000 meters, then turns around and shoots his gun, putting a hole right through his hat. How did he do it?
Hint:
I Exist Where There Is Light Riddle
Hint:
David Is 6 Years Old Riddle
Hint:
David: 6
Lauren: 3
David is 3 years older than Lauren.
So when David is 100 Lauren is 97.
Answer: 97 Did you answer this riddle correctly?
YES NO
Lauren: 3
David is 3 years older than Lauren.
So when David is 100 Lauren is 97.
Answer: 97 Did you answer this riddle correctly?
YES NO
What Can You Hold In Your Right Hand Riddle
Hint:
A Terrorist Took Over A Plane Riddle
A terrorist hijacks a plane with 10 passengers and there is lots of gold in the plane.
After talking the gold, he asked the government officials for 11 parachutes.
He killed all the passenger so that no one can identify him, take one parachute and jumps off.
Was he stupid to ask for 11 parachutes if he need only one?
After talking the gold, he asked the government officials for 11 parachutes.
He killed all the passenger so that no one can identify him, take one parachute and jumps off.
Was he stupid to ask for 11 parachutes if he need only one?
Hint:
He was genius.
Officials must have thought he was jumping with a hostage, they would never risk giving him a faulty parachute. Did you answer this riddle correctly?
YES NO
Officials must have thought he was jumping with a hostage, they would never risk giving him a faulty parachute. Did you answer this riddle correctly?
YES NO
My Life Can Last Some Hours Riddle
Hint:
7 Candles Riddle
Hint:
7, we asked 'how many candles' not 'how many lit candles' Did you answer this riddle correctly?
YES NO
YES NO
A Train Leaves From Halifax Riddle
Hint:
Both trains would be at the same spot when they meet therefore they are both equally close to Halifax. Did you answer this riddle correctly?
YES NO
YES NO
6 Pens Riddle
Hint:
Add Your Riddle Here
Have some tricky riddles of your own? Leave them below for our users to try and solve.