## A Multiplication Based Logic Puzzle

### 76 and Level 1

76 is a composite number. 76 = 1 x 76, 2 x 38, or 4 x 19. Factors of 76: 1, 2, 4, 19, 38, 76, Prime factorization: 76 = 2 x 2 x 19, which can also be written 2² x 19.

76 is never a clue in the FIND THE FACTORS puzzles.

This week’s puzzles and last week’s solutions: 10 Factors 2014-03-31

### 75 and Level 6

75 is a composite number. 75 = 1 x 75, 3 x 25, or 5 x 15. Factors of 75: 1, 3, 5, 15, 25, 75. Prime factorization: 75 = 3 x 5 x 5, which can also be written 75 = 3 x 5².

75 is never a clue in the FIND THE FACTORS puzzles.

This week’s puzzles for you to solve

### 74 and Level 5

74 is a composite number. 74 = 1 x 74 or 2 x 37. Factors of 74: 1, 2, 37, 74. Prime factorization: 74 = 2 x 37.

74 is never a clue in the FIND THE FACTORS puzzles.

This week’s puzzles for you to solve

### 73 and Once

73 is a prime number. 73 = 1 x 73. Its only factors are 1 and 73. Prime factorization: none.

How do we know that 73 is a prime number? The square root of 73 is an irrational number approximately equal to 8.54. If 73 were not a prime number, then it would be divisible by at least one prime number less than or equal to 8.54. Since 73 is not divisible by 2, 3, 5, or 7, it is a prime number.

73 is never a clue in the FIND THE FACTORS puzzles.

I very much enjoyed going to the school of fairies today where even butterflies can learn to multiply. The author translates a sweet poem from Hungarian into English. I hope you will remember the poem’s encouraging words whenever you try to solve one of my multiplication table puzzles or any other task that challenges you in life.

This was one of the most difficult songs to translate so far, because the original Hungarian poem plays with ‘Egyszeregy’ which means 1*1 and is the common name for the multiplication table, is used to express what ‘easy as ABC’ is in English, and means ‘Once upon’ at the same time. I could have used ‘one time’ in English as well but it doesn’t invoke multiplying that strongly, plus it’s rhytmically off. I could have used the ABC and go for literacy instead of math, but the rhytm isn’t good either. Plus in Hungarian this little story is about the fairies who go over the ‘Glass mountain’ which is the mythical location of fairy tales in Hungarian but doesn’t exist in English and the best substitute that came to my mind was ‘oves the rainbow’. But as you may guess, that doesn’t fit rhytmically either (plus there aren’t any proper…

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### 72 and Level 4

72 is a composite number. 72 = 1 x 72, 2 x 36, 3 x 24, 4 x 18, 6 x 12, or 8 x 9. Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. Prime factorization: 72 = 2 x 2 x 2 x 3 x 3, which can also be written 2³ x 3²

Sometimes 72 is a clue in the Find the Factors puzzles. Even though it has many other factors, we use only 8 x 9 for the FIND THE FACTORS 1-10 puzzles and 8 x 9 or 6 x 12 for the FIND THE FACTORS 1-12 puzzles.

This week’s puzzles for you to solve

### 71 and Level 3

71 is a prime number. 71 = 1 x 71. Its only factors are 1 and 71. Prime factorization: none.

How do we know that 71 is a prime number? The square root of 71 is an irrational number approximately equal to 8.43. If 71 were not a prime number, then it would be divisible by at least one prime number less than or equal to 8.43. Since 71 is not divisible by 2, 3, 5, or 7, it is a prime number.

71 is never a clue in the FIND THE FACTORS puzzles.

This week’s puzzles for you to solve

A Logical Approach to the Solution: Find the column or row with two clues and find their common factor. Write the corresponding factors in the factor column and factor row.  Because this is a level three puzzle, you have now written a factor at the top of the factor column. Continue to work from the top of the factor column to the bottom, finding factors and filling in the table as you go:

A Logical Approach to find the factors: Find the column or row with two clues and find their common factor. Write the corresponding factors in the factor column and factor row.  Because this is a level three puzzle, you have now written a factor at the top of the factor column. Continue to work from the top of the factor column to the bottom, finding factors and filling in the table one row at a time as you go:

### 70 and Level 2

70 is a composite number. 70 = 1 x 70, 2 x 35, 5 x 14, and 7 x 10. Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70. Prime factorization: 70 = 2 x 5 x 7.

Sometimes 70 is a clue in the FIND THE FACTORS 1 – 12 puzzles. Even though it has other factors, we only use 70 = 7 x 10 in the puzzles.

This week’s puzzles for you to solve

Here are the factors for today’s puzzle: