A wise king devised a contest to see who would receive the Princess’ hand in marriage. The Princess was put in a 50 x 50 foot carpeted room. Each of her four suitors were put in one corner of the room with a small box to stand on. The first one to touch the Princess’ hand would be the winner and become the new King.
The rules were the contestants could not walk over the carpet, cross the plane of the carpet, or hang from anything; nor could they use anything but their body and wits (i.e. no magic, telepathy, nor any items such as ladders, block and tackles etc). One suitor figured out a way and married the Princess and became the new King. What did he do?
A man and his son had a terrible car accident and were rushed to the hospital. The man died on the way, but the son was still barely alive. When they arrived, an old gray surgeon was called in to operate. Upon seeing the young boy, the surgeon said, “I can’t operate – this is my son.”
The man in the picture is the onlooker’s son. Since he doesn’t have any brothers or sisters, the statement my father’s son can only be himself. A shortened version would be this man’s father is me, making him the father of the man in the picture.
A man is traveling with a fox and two chickens, if he leaves the fox alone with the chickens the fox will eat the chickens. He comes to a river and needs to cross it, he finds a small boat that can carry only him and one animal, how does he get himself, the fox and two chickens across the river safely?
Take the fox over, return with nothing. Go over with one chicken, return with the fox. Go over with the second chicken, return with nothing. Finally, take the fox over.
The trick is that the word “dead” represents a number in hexadecimal. That number in base 10 is 57005, and adding one more to include yourself gives you: 57005 + 1 = 57006.
You will hang me. If they hang him, then the statement was true and they could only hang him for telling a lie. If they shoot him, then it makes the statement a lie and they were only to shoot him for telling the truth. An alternate solution is to say, “You will not shoot me,” leading to the same quandary for the killers.
A man can make perfect counterfeit bills. They look exactly like real ones, they’re made of exactly the same materials, made the same way, everything. So perfect, one could pretty much call them real bills. One day he successfully makes a perfect copy of another bill. However, he gets caught when he tries to use the copy. How is this possible?
As a counterfeiter, he had lots of counterfeit bills around and he accidentally used one of them as his original. So he made a perfect copy of a counterfeit bill.
During WWII, there was a bridge connecting Germany and Switzerland, and on the German side, there was a sentry tower with a guard in it. He would come out every three minutes to check on the bridge, and he had orders to turn back anyone who tried to get into Germany, and shoot anyone trying to escape without a pass. There was a woman who desperately needed to get into Switzerland, and she knew she didn’t have time to get a pass. It would take her at least six minutes to cross the bridge, but she managed to do it. How?
She walked on the bridge towards Switzerland for 3 minutes and just as the guard was about to come out, she turned around walking back to Germany. The guard saw her and asked for her pass but she didn’t have one and was sent back (or what the guard thought was back) to Switzerland. In her case it was the very country she wanted to go to.
A princess is as old as the prince will be when the princess is twice the age that the prince was when the princess’s age was half the sum of their present ages.
This one took a while to figure out and there are numerous valid ways of finding the answer.
Here is the solution I came up with
I created the following table from the riddle:
Current
Future
Past
Princess
x
2z
(x+y)/2
Prince
y
x
z
I then created three equations, since the difference in their age will always be the same.
d = the difference in ages
x – y = d
2z – x = d
x/2 + y/2 – z = d
I then created a matrix and solved it using row reduction.
x
y
z
1
-1
0
d
-1
0
2
d
.5
.5
-1
d
It reduced to:
x
y
z
1
0
0
4d
0
1
0
3d
0
0
1
5d/2
This means that you can pick any difference you want (an even one presumably because you want integer ages).
Princess age: 4d
Prince age: 3d
Ages that work
Princess
Prince
4
3
8
6
16
12
24
18
32
24
40
30
48
36
56
42
64
48
72
54
80
60
To see other solutions check out the comments from when I posted this on my blog.
You have two buckets. One holds exactly five gallons and the other three gallons. How can you measure exactly four gallons of water into the five gallon bucket?
Assume you have an unlimited supply of water and that there are no measurement markings of any kind on the buckets.