A Multiplication Based Logic Puzzle

Posts tagged ‘puzzles’

669 and Level 4

Since all its digits are divisible by 3, obviously 669 is divisible by 3.

222 + 223 + 224 = 669. Thus 669 is the sum of 3 consecutive numbers. Prime factor 223 is the middle number in the sum.

669 Puzzle

Print the puzzles or type the solution on this excel file: 12 Factors 2015-11-02

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  • 669 is a composite number.
  • Prime factorization: 669 = 3 x 223
  • 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 669 has exactly 4 factors.
  • Factors of 669: 1, 3, 223, 669
  • Factor pairs: 669 = 1 x 669 or 3 x 223
  • 669 has no square factors that allow its square root to be simplified. √669 ≈ 25.865034.

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669 Logic

Ricardo shows the solution here:

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329 and A Last Minute Gift

  • 329 is a composite number.
  • Prime factorization: 329 = 7 x 47
  • 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 329 has exactly 4 factors.
  • Factors of 329: 1, 7, 47, 329
  • Factor pairs: 329 = 1 x 329 or 7 x 47
  • 329 has no square factors that allow its square root to be simplified. √329 ≈ 18.138

Here’s a puzzle that could be a last minute gift. If there is a child in you life who has recently become familiar with the multiplication table, put this puzzle in his or her stocking! It is as easy as the puzzles get.

2014-51 Level 1

Print or type on this week’s puzzles using this excel file: 10 Factors 2014-12-22

2014-51 Level 1 Factors

Last year on Christmas Eve I offered a free last minute gift, a puzzle booklet, but I discovered that most people take care of their last minute gift-giving a couple of days sooner than that. Still this last minute gift could be sent electronically and you can’t beat the price.

I also learned that margins in excel can move so the booklet didn’t always print up as nicely as I wanted. I’m still recovering from surgery so this year I simply revised that same booklet.

I saved the booklet as Factor Holiday pdf to eliminate those printing issues.  In pdf, the lines on the puzzles became quite dark so I don’t like the way they look as much, but I’ll live with it.

The booklet is also available in Factor Holiday excel if you prefer to type your answers directly on the computer. You can try printing it off of excel as well, but I can’t guarantee what the margins will do at any given time.

Here’s a copy of the puzzle booklet’s cover with my sincere holiday greetings for all of you:

2013 Puzzle Holiday

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 (2^3) x (3^2).

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.

2014-12 Level 4

This week’s puzzles for you to solve

2014-12 Level 4 Logic

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68 and Happy Saint Patrick’s Day!

68 is a composite number. 68 = 1 x 68, 2 x 34, or 4 x 17. Factors of 68: 1, 2, 4, 17, 34, 68. Prime factorization: 68 = 2 x 2 x 17, which can also be written (2^2) x 17.

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

2014-11 Level 6

All Previously Published Puzzles

I survived my daughter’s wedding. The last of our out-of-state visitors will be going home tomorrow. AND my computer that broke and spent a week in the shop is working again. I will publish six new puzzles next Monday.

2014-11 Level 6 Logic

64 and Can You See the Logic Here?

64 is a composite number, and it is 8 squared. 64 = 1 x 64, 2 x 32, 4 x 16, or 8 x 8. Factors of 64: 1, 2, 4, 8. Prime factorization: 64 = 2 x 2 x 2 x 2 x 2 x 2, which can also be written 64 = 2^6.

Since √64 = 8, a whole number, 64 is a perfect square.

Sometimes 64 is a clue in the FIND THE FACTORS puzzles. Even though it has other factors, when it is a clue, the factors are always 8 x 8.

2014-08 Level 6

All Previously Published Puzzles

2014-08 Level 6 Answer

This solution is complicated, but here is a logical explanation:

There are only two 3s available, so at most one 9 can be 3 x 3.

Can both 9s be 9 x 1? If both were, then both 1s would be used, leaving 8 = 2 x 4 and 10 = 2 x 5 as the only possibilities for 8 and 10. But if both 9s were 9 x 1, then the 18 in the same row as the 9 would have to be 18 = 9 x 2, and that would use too many twos. Therefore, EXACTLY ONE of the nines can use 9 = 9 x 1.

Since one 9 = 3 x 3, using both 3s, 30 must equal 5 x 6. And since both 30 and 50 must use both 5s, 10 must equal 10 x 1.

Since 10 = 10 x 1 and a 9 = 9 x 1, 8 must equal 2 x 4. So now finally we can begin filling out the puzzle:

2014-08 Level 6 Logic

63 and Twelve Quick Clues

 

63 is a composite number. 63 = 1 x 63, 3 x 21, or 7 x 9. Factors of 63: 1, 3, 7, 9, 21, 63. Prime factorization: 63 = 3 x 3 x 7, which can also be written 63 = (3^2) x 7.

Sometimes 63 is a clue in the FIND THE FACTORS puzzles. Even though it has other factors, the only multiplication fact we use is 7 x 9 = 63.

2014-07 Level 6

All Previously Published Puzzles

2014-07 steps

62 and Love: Challenging But Worth It

62 is a composite number. 62 = 1 x 62 or 2 x 31. Factors of 62: 1, 2, 31, 62. Prime factorization: 62 = 2 x 31.

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

valentine 2014

All Previously Published Puzzles

square root mems

 

Here is the logic to solve the puzzle & a chart showing one way to get the solution:

9 has to be the factor of both the 27 and the 63.  Therefore 3 x 6 = 18, (not 2 x 9).

3 is one of the factors of both the 18 and the 27.  Therefore 9 x 1 = 9, (not 3 x 3).

Valentine 2014 steps

 

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