Fun Science / Brain Teazers
This is a page that contains various riddles, questions and quizzes that I have gathered over the years. They can help your brain to stay fresh. Don’t feel embarrassed if you cannot solve them :-)
The numbers inside the brackets [ ] indicate the difficulty on a 1 - 10 scale.
1=2 [4]
x^2 =x+x+x+x+x+…. (x times)
Taking the derivative in both sides we get: 2x = 1+1+1+1+ … (x times)
But since 1 + 1 + 1 + 1 … (x times) = x
Then 2x = x 2 = 1
What is she doing now? [3]
In 3 years a mother will be 12 times older than her child now. In 9 years she will be 4 times older than her child now.
4 4’s [9]
With 4 4’s and any mathematical symbol that you think it’s useful, try to create the number 33. For example, 32 = 4( 4 + Sqrt[4]Sqrt[4] ) , 31 = 4! + (4!+4)/4.
I first dealt with this problem in high school, where I managed to create all numbers from 1 to 100, except for 3-4 cases. 33 was the smallest number that I couldn’t figure it out, despite days of thinking. Since then 33 is my favorite number. I came across the solution years later, realizing that such games where purposeless since I could create any number I wanted.
Lock & Key [6]
You want to send a valuable object to a friend. You have a box which is more than large enough to contain the object. You have several locks with keys. The box has a locking ring which is more than large enough to have a lock attached. But your friend does not have the key to any lock that you have. Note that you cannot send a key in an unlocked box, since it might be copied.
Missing Letter [8]
Which is the letter missing from the following sequence?
A A A A ? A A A A A A
Hint: The answer is not A.
Sangria and the Milk [5]
There is a bottle that contains one litre of Sangria. Another bottle contains one litre of milk. We take a cup full of Sangria from its bottle and pour it over inside the milk bottle. We shake the mixture well. We then take a cup full of that mixture and pour it back to the Sangria bottle.
Is there now more, less, or equal amount of Milk dissolved inside the Sangria bottle, compared to amount of Sangria dissolved in the Milk bottle?
The Missing Dollar [3]
Three guys paid $30 for staying at a hotel room. The next day the manager realizes that he overcharged them, and gives $5 to a bellhop to return to the guests. Th bellhop, realizing that the 3 guys are unaware of the overcharge amount, keeps $2 to himself and returns $1 to each guest. Thus, each guest has now paid $9 (3 x $9 = $27), plus the $2 that the bellhop kept to himself, for a total of $29.
What happened to the last dollar?
The fake coin [9]
You have a balance scale (i.e. a scale that indicates which of two sides is heavier, without indicating the exact weight differential) and 12 coins, one of which is fake. The fake coin can be either lighter or heavier than the rest, which are identical to each other.
Can you find the fake coin in 3 weighings?
Hint: You can first try the same problem when there are 3 coins and 2 weighings.
A Dozen Sum [2]
Can you circle 4 numbers below, such that their sum is equal to 12?
The Almond Garden [10]
Two numbers in the interval [3,100] are chosen. Their product and sum are calculated, which are given, respectively, to two persons coincidentally named Mr. Product and Mr. Sum. The following discussion takes place between them:
- Mr. P: I cannot find the numbers.
- Mr. S: Me neither, but I knew that you couldn’t find them.
- Mr. P: Now that you mentioned that, I can find the two numbers!
- Mr. S: Since you found them, I can now find them myself too!
Which are the two numbers that were selected?
Hint: The above dialogue could have taken place only for a given pair of numbers.
