A Multiplication Based Logic Puzzle

Posts tagged ‘consecutive prime numbers’

532 and Level 3

532 is the sum of consecutive prime numbers 263 and 269.

532 is also the 19th pentagonal number.

532 Puzzle

Print the puzzles or type the solution on this excel file: 10 Factors 2015-06-22

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  • 532 is a composite number.
  • Prime factorization: 532 = 2 x 2 x 7 x 19, which can be written 532 = (2^2) x 7 x 19
  • The exponents in the prime factorization are 1, 2, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 x 2 x 2 = 12. Therefore 532 has exactly 12 factors.
  • Factors of 532: 1, 2, 4, 7, 14, 19, 28, 38, 76, 133, 266, 532
  • Factor pairs: 532 = 1 x 532, 2 x 266, 4 x 133, 7 x 76, 14 x 38, or 19 x 28
  • Taking the factor pair with the largest square number factor, we get √532 = (√4)(√133) = 2√133 ≈ 23.065125

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A Logical Approach to solve a FIND THE FACTORS puzzle: Find the column or row with two clues and find their common factor. Write the corresponding factors in the factor column (1st column) and factor row (top 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 factor column and the factor row one cell at a time as you go.

532 Factors

 

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499 and Level 5

499 is the sum of a nice bunch of consecutive prime numbers:

  • 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 = 499. That’s 17 consecutive primes.

499 Puzzle

Print the puzzles or type the solution on this excel file: 12 Factors 2015-05-18

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  • 499 is a prime number.
  • Prime factorization: 499 is prime.
  • The exponent of prime number 499 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 499 has exactly 2 factors.
  • Factors of 499: 1, 499
  • Factor pairs: 499 = 1 x 499
  • 499 has no square factors that allow its square root to be simplified. √499 ≈ 22.3383079

How do we know that 499 is a prime number? If 499 were not a prime number, then it would be divisible by at least one prime number less than or equal to √499 ≈ 22.3383. Since 499 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, or 19, we know that 499 is a prime number.

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499 Logic

497 and Level 3

497 is the sum of a five consecutive prime numbers: 89 + 97 + 101 + 103 + 107 = 497.

497 Puzzle

Print the puzzles or type the solution on this excel file: 12 Factors 2015-05-18

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  • 497 is a composite number.
  • Prime factorization: 497 = 7 x 71
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 497 has exactly 4 factors.
  • Factors of 497: 1, 7, 71, 497
  • Factor pairs: 497 = 1 x 497 or 7 x 71
  • 497 has no square factors that allow its square root to be simplified. √497 ≈ 22.2934968

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A Logical Approach to solve a FIND THE FACTORS puzzle: Find the column or row with two clues and find their common factor. Write the corresponding factors in the factor column (1st column) and factor row (top 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 factor column and the factor row one cell at a time as you go.

497 Factors

479 and Level 6

479 is the sum of nine consecutive prime numbers.

37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 = 479.

479 Puzzle

Print the puzzles or type the solution on this excel file: 10 Factors 2015-04-27

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  • 479 is a prime number.
  • Prime factorization: 479 is prime.
  • The exponent of prime number 479 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 479 has exactly 2 factors.
  • Factors of 479: 1, 479
  • Factor pairs: 479 = 1 x 479
  • 479 has no square factors that allow its square root to be simplified. √479 ≈ 21.88607

How do we know that 479 is a prime number? If 479 were not a prime number, then it would be divisible by at least one prime number less than or equal to √479 ≈ 21.8861. Since 479 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, or 19, we know that 479 is a prime number.

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479 Logic

Just a Little 473 Cake

Today is our wedding anniversary. Today I tried to spend my time with my husband instead of the computer. Hence this is a very short and plain post.

The middle digit of 473 equals the sum of the other two digits which means that 473 can be evenly divided by 11.

Five years from now I could make one of these cakes for our anniversary!

473 is the sum of some consecutive prime numbers two different ways. See if you can find them yourself. Then check the comments to see if you were right.

  • 473 is a composite number.
  • Prime factorization: 473 = 11 x 43
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 473 has exactly 4 factors.
  • Factors of 473: 1, 11, 43, 473
  • Factor pairs: 473 = 1 x 473 or 11 x 43
  • 473 has no square factors that allow its square root to be simplified. √473 ≈ 21.74856

457 A Pythagorean Triple Logic Puzzle

457 = 4² + 21², and it is the hypotenuse of the primitive Pythagorean triple 168-425-457. Also, 457 is the sum of some consecutive prime numbers. One of my readers posted those primes in the comments.

A long time ago I decided that Pythagorean triples could make a great logic puzzle, so I created one. You can see it directly underneath the following directions:

This puzzle is NOT drawn to scale. Angles that are marked as right angles are 90 degrees, but any angle that looks like a 45 degree angle, isn’t 45 degrees. Lines that look parallel are NOT parallel. Shorter looking line segments may actually be longer than longer looking line segments. Most rules of geometry do not apply here: in fact non-adjacent triangles in the drawing might actually overlap.

No geometry is needed to solve this puzzle. All that is needed is the table of Pythagorean triples under the puzzle. The puzzle only uses triples in which each leg and each hypotenuse is less than 100 units long. The puzzle has only one solution.

If any of these directions are not clear, let me know in the comments. I will NOT be publishing the solution to this puzzle, but I will allow anyone who desires to put any or all of the missing values in the comments. Also, the comments will help me determine if I should publish another puzzle like this one.

Good Luck!

457 Puzzle

Sorted Triples

Print the puzzles or type the solution on this excel file:  10 Factors 2015-04-13

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  • 457 is a prime number.
  • Prime factorization: 457 is prime.
  • The exponent of prime number 457 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 457 has exactly 2 factors.
  • Factors of 457: 1, 457
  • Factor pairs: 457 = 1 x 457
  • 457 has no square factors that allow its square root to be simplified. √457 ≈ 21.3776

How do we know that 457 is a prime number? If 457 were not a prime number, then it would be divisible by at least one prime number less than or equal to √457 ≈ 21.3776. Since 457 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, or 19, we know that 457 is a prime number.

449 and Level 1

449 is the sum of consecutive prime numbers. How many and what are they? Check the comments to see the answer.

449 Puzzle

Print the puzzles or type the factors on this excel file:  12 Factors 2015-04-06

449 = 20² + 7² so 449 is the hypotenuse of a Pythagorean triple. That triple will be 2(20)(7), 20² – 7², 20² + 7² which is primitive triple 280-351-449.

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  • 449 is a prime number.
  • Prime factorization: 449 is prime.
  • The exponent of prime number 449 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 449 has exactly 2 factors.
  • Factors of 449: 1, 449
  • Factor pairs: 449 = 1 x 449
  • 449 has no square factors that allow its square root to be simplified. √449 ≈ 21.1896

How do we know that 449 is a prime number? If 449 were not a prime number, then it would be divisible by at least one prime number less than or equal to √449 ≈ 21.1896. Since 449 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, or 19, we know that 449 is a prime number.

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449 Factors

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