Math puzzles:

• The first puzzle is fairly easy:
  • Consider the sequence: 2 3 7 2 6 3 5 1 4 1 7 6 5 4
  • In between the 1's there is just a single number (4)
  • In other words, in between the 1's there is one number
  • Similarly, in between the 2's there are two numbers
  • And in between the 3's there are three numbers
  • ...
  • In between the 7's there are seven numbers.
  • Here is the problem:
  • Rearrange the numbers 1 1 2 2 3 3 so that:
  • In between the 1's there is one number
  • and in between the 2's there are two numbers
  • and in between the 3's there are three numbers.
  
  
• The second puzzle is fairly difficult:
  • What is the next number in the following sequence:
    • 0, 4, 8, 21, 52, 65, 96, ?
  
  
• 3rd puzzle:
  • What is the next number in the following sequence:
    • 1, 32, 81, 64, 25, 6, ?
  
  
• 4th puzzle:
  • Find primes x, y and z such that 2x + 3y + 6z = 78
  
  
• 5th puzzle:
  • What is the next number in the following sequence:
    • 61, 52, 63, 94, 46, ?
  
  
• 6th/7th puzzles:
  • Fill in the blanks with PLUS or MINUS to make the equations true:
    
    
    
    
  
  
• 8th puzzle:
  • In a room there are three people.
  • One person is always honest. One always lies.
  • And there is a spy who is sometimes honest and sometimes tells lies.
  • You ask each one who they are. Here are their answers:
  • The first person says, "I am the truth teller."
  • The second person says, "I am the liar."
  • The third person says, "I am the spy."
  • But which person is really the truth teller? And which one is the liar and the spy?
  
  
• 9th puzzle:
  • In a room there are three people.
  • One person is always honest. One always lies.
  • And there is a spy who is sometimes honest and sometimes tells lies.
  • You ask each one who they are. Here are their answers:
  • The first person says, "I am not the truth teller."
  • The second person says, "I am not the liar."
  • The third person says, "I am not the spy."
  • But which person is really the truth teller? And which one is the liar and the spy?
  
  
• 10th puzzle:
  • There are three people called A, B, and C.
  • One of them is a knight, one is a knave, and one is a spy.
  • The knight always tells the truth, the knave always lies,
  • and the spy sometimes lies and sometimes tells the truth.
  • A says: "C is a knave."
  • B says: "A is a knight."
  • C says: "I am the spy."
  • Who is the knight, who is the knave, and who is the spy?
  
  
• 11th puzzle:
  • Place one NON-zero digit in each box below so the resulting equation is true:
    
    
  
  
• 12th puzzle:
  • Using each of the digits 1, 2, 3, ... 9 exactly once, fill in the boxes so that the product is an integer:
    
    

    Solution

  
  
• Function problems
  
  
• Equation problems
  
  
• Nice trigonometric problem
  
  
• Sudoku problems
  
  
• Square root simplification problem

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The following sequence is related to the 1st puzzle.
I made it. I think it is so beautiful.

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In general, matrix multiplication is not commutative.
But I created a simple example of 2 matrices without repeated numbers that are commutative in multiplication.

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Math jokes:

• Klein bottle for rent -- enquire within.

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Frankenstein numbers

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