Prove that for all prime numbers p > 3, (p2 – 1) is a multiple of 24.
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Brain Teasers and Puzzles
Brain teasers, puzzles, riddles, and other challenges
Most Frequent Digit
What is the most frequent digit among the numbers between 1 and 1000 (inclusive)? Consider only base-10 whole numbers.
Continue reading “Most Frequent Digit”Same Birthday in Line
There is a long line of people waiting to see a new movie. They announce that the first person to have the same birthday as someone standing before them in the line gets to meet one of the actors in the movie.
What place in line would maximize your chances of winning? Assume birthdays are uniformly distributed through the year.
Continue reading “Same Birthday in Line”Prison Keys Strategy
A prison warden was feeling capricious and played a game with the prison keys:
- Each prisoner is handed a key to another prisoner’s cell.
- Each prisoner will know which other prisoner was initially given the key to their cell (but does not know whose key they were handed).
- Each day, when all prisoners are out of their cells and no one is watching, each prisoner is allowed to place keys in another prisoner’s cell.
- Each night, each prisoner can collect any keys placed in their cell.
- The prisoners can summon the warden when they’re sure everyone has their own key – but if they are wrong, they’re immediately executed.
- The prisoners can discuss a strategy beforehand but cannot communicate in any way after keys are handed out.
What is the fewest number of days it would take for the prisoners to be sure everyone has their key? What was the strategy to achieve this?
View SolutionDigital Sum of the Sum
The digital sum of a number is just the sum of the individual digits. E.g., the digital sum of 123 is 1 + 2 + 3 = 6.
- The digital sum of x is 42
- The digital sum of y is 67
- When x and y are added, you have to “carry the 1” exactly five times (e.g., if you add 8 and 9, you “carry the 1” once to get a “1” in the tens digit, thereby getting 17)
What is the digital sum of z = x + y?
Continue reading “Digital Sum of the Sum”If you share me you haven’t got me
If you have me, you want to share me. If you share me, you haven’t got me. What am I?
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A secret
Many people who have a secret want to share it. But if you share a secret, it is no longer secret, so you haven’t got it anymore.
Sharing Game Theory Puzzle
In this sharing game theory puzzle, 3 friends take turns taking from a jar of 1000 candies to share. For example, the 1st friend could take 500 candies, then the 2nd friend could take 400, and the 3rd friend would take the remaining 100.
No one wants to be seen as greedy, but no one wants to end up with the fewest candies either. As such, their goals are (in order of preference):
- Do not end up with the most candies, nor the fewest candies (a tie for most or fewest also fails this condition)
- End up with as many candies as possible
All of them are logical, rational, know each other’s goals, but cannot communicate before or during sharing. How many candies should each friend end up with?
View SolutionI Am Normally Below You Riddle
I am a 5-letter word. I am normally below you.
If you remove my 1st letter, I am normally above you.
If you remove my 1st and 2nd letters, I am all around you.
View SolutionRebus Puzzle 18
What common word or phrase is this rebus referring to?
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Solution
Read between the lines
Rock Paper Scissors Puzzle
A rock paper scissors puzzle:
- Anya played 10 games of rock paper scissors against Blake
- Each time there was a winner (no ties)
- Anya used rock 2 times, paper 2 times, and scissors 6 times, but you don’t know the order
- Blake used rock 2 times, paper 4 times, and scissors 4 times, but you don’t know the order
How many games did each player win?
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