Four years ago, Meg put a nail on a tree in order to mark her height. If the tree grows 10 inches per year, and currently the nail is 5 inches lower than Meg, how much has Meg grown over these four years?
You are playing a game of Bridge. Which probability is greater – that you and your partner do not have any spades, or that you and your partner have all the spades in the game?
SOLUTION
You and your partner do not have any spades if and only if your opponents have all the spades. Therefore the probabilities are equal.
A person enters a pet shop and sees a beautiful parrot. The seller guarantees him that the bird repeats everything it hears, so the person buys it. However, when he goes back home and tests the bird, it turns out that it doesn’t say a word. The buyer goes to the shop to complain to the seller, but the seller argues he has not lied. How is this possible?
A Sheikh dies, leaving behind three sons, 17 camels, and the following order:
1. The oldest son shall inherit one in two camels. 2. The middle son shall inherit one in three camels. 3. The youngest son shall inherit one in nine camels.
Now the three sons do not know what to do. They ask an old friend of the family for advice, and he finds a solution. What does the friend propose?
SOLUTION
The friend lent them one camel to make the camels 18. The first son took 9 camels, the second son took 6 camels, the third son took 2 camels. Then the friend took back his camel.
There are five pirates, one monkey, and lots of coconuts on an island. The pirates are supposed to share the coconuts on the next day, but while everybody is sleeping, the first pirate gives 1 coconut to the monkey, splits the remaining coconuts into 5 equal piles, and secretly keeps one of the piles for himself. Later, the second pirate does the same, then the third one, the fourth one, and the fifth one. On the morning, the pirates wake up and split all the remaining coconuts in five, leaving one last coconut for the monkey. What is a possible number for the number of coconuts on the island?
SOLUTION
Notice that if we find a certain number of coconuts which works, then we can add 56 and get a new one. Now imagine the pirates start with -4 coconuts, i.e. they have a total loan of 4 coconuts. Every time a pirate wakes up, he gives 1 coconut to the monkey, which makes the total loan 5 coconuts. Then the pirate keeps a loan of 1 coconut for himself and leaves -4 coconuts. Now we just add 56 coconuts to -4 to make the number positive and get 56 – 4 coconuts as a possible answer.
Researchers have discovered a strong positive correlation between performance in spelling bees and contestants’ shoe sizes. Can you find an explanation for this?
SOLUTION
Older students have bigger feet and perform better at spelling bee contests.
James sent this beautiful photo to a contest, hoping he will win first prize. The contest organizers, however, realized that the photo was fake and disqualified James. How did they figure out the picture was not real?
When do the hour and the minute hands of the clock lie on top of each other, and also between the numbers 1 and 2?
SOLUTION
One such time is around 1:05 – at 1 o’clock and 5.454… minutes. This can be easily found by solving the linear equation x = 12(x – 5) => x=60/11.
Another time you possibly didn’t think about is 12:00 o’clock. At that time, the hour and minute hands are on top of each other and just between the two digits of the number 12.
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