A Multiplication Based Logic Puzzle

Archive for January, 2014

53 and Animated Gif FIND THE FACTORS Level 5

53 is a prime number. 53 = 1 x 53. Its only factors are 1 and 53. Prime factorization: none.

How do we know that 53 is a prime number? The square root of 53 is an irrational number approximately equal to 7.28. If 53 were not a prime number, then it would be divisible by at least one prime number less than or equal to 7.28. Since 53 is not divisible by 2, 3, 5, or 7, it is a prime number.

I’m a mother and a grandmother. My most recent grandson, Oliver, was born three days ago on Tuesday.

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Steve Wilhite, the creator of gif graphics format, said,”Choosy mothers choose GIF.” I think that can apply to grandmothers, too.

I made my very first animated gif! You can see the factors from last week’s level 5 puzzle appear one by one right before your eyes! I set the gif at the slowest possible setting, but it still goes fairly fast. The puzzle is solved from start to finish in about 15 seconds.

FIND THE FACTORS 403-5

Here is this week’s level 5 puzzle. To solve it, write the numbers from 1 to 12 in the top row and again in the first column so that the numbers you write are the factors of the given clues. There is only one solution.

2014-04 Level 5

This week’s puzzles are available in an excel file here. If you have a spreadsheet program on your computer, you can access it. If you enable editing in excel, you can type your answers directly onto the puzzle, and you can also easily print the puzzles.

Here are the factors from last week’s level 5 puzzle:

2014-03 Level 5 Answer

How were those factors found? Look at the animated gif above or click here to see the puzzle being solved, or you can look at the chart below for a slightly different way to solve it.

2014-03 L5 steps

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52 and Maths in the snow

52 is a composite number. 52 = 1 x 52, 2 x 26, or 4 x 13. Factors of 52: 1, 2, 4, 13, 26, 52. Prime factorization: 52 = 2² x 13.

52 is never a clue in the FIND THE FACTORS 1- 10 or 1- 12 puzzles.

Here are some incredible and beautiful sketches in the snow. These pictures must have been taken from an airplane or helicopter. Be sure to click on the picture so you can see many other sketches including a gorgeous fractal.

Matters Mathematical

Rule number one of this blog: Maths is fun. So here is a guy who is having fun sketching mathematical shapes in the snow. (click on the photo to see more of his mindblowing snow graphs)
Simon-Beck-Snow-art2

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51 and Magic forcing grid – Maths Magic

51 is a composite number. 51 = 1 x 51 or 3 x 17. Factors of 51: 1, 3, 17, 51. Prime factorization: 51 = 3 x 17.

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

Mathematics is full of magic, sometimes more than we even expected. There appears to be a connection between this math trick and 4 x 4 magic squares. I will be interested to see if anyone can form a 4 x 4 magic square from the information provided by The Science Magician in this post. There are 880 ways to make a 4 x 4 magic square, so it seems like it would still be a lot of work. This same process works on a 3 x 3 square and results in numbers that add up to 15 in every case.

The Science Magician - Dr Matt Pritchard

What’s the effect?

A 4×4 square grid is created on a piece of paper with numbers from 1-16 (see top left hand picture). Spectators choose 4 numbers at random from the grid and the total always equals 34.

What you need?

  • Pen and paper

What’s the method?

There was one crucial detail left out from the description of the effect. When the first number is chosen and circled, the remaining numbers on that row and column are crossed out (see the top right picture). grid16a

There is now only a choice of 9 numbers for the second spectator to choose from. Again the choice is circled and the row and column is crossed out. For the third choice there are only 4 numbers remaining. The final choice isn’t a choice at all as there’s only one number that hasn’t been circled or crossed out. The total of the 4 chosen numbers…

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50 and Multiples

Multiples and factors are related.

For example, 50 is a multiple of all these numbers: 1, 2, 5, 10, 25, and 50.

And 1, 2, 5, 10, 25, and 50 are all factors of 50.

50 is a composite number. 50 = 1 x 50, 2 x 25, or 5 x 10. Factors of 50: 1, 2, 5, 10, 25, 50. Prime factorization: 50 = 2 x 5 x 5, which can also be written 2 x 5².

Sometimes 50 is a clue in the FIND THE FACTORS puzzles. Even though it has other factors, we only use 50 = 5 x 10 to fill in the table.

Each of the clues inside this puzzle are MULTIPLES of a number from 1 to 12. Can you write every number from 1 to 12 in the top row as well as in the first column so that the clues are multiples of the numbers that you write?

2014-04 Level 4

This week’s puzzles are available in an excel file here. If you have a spreadsheet program on your computer, you can access it. If you enable editing in excel, you can type your answers directly onto the puzzle, and you can also easily print the puzzles.

Here are the factors to last week’s level 4 puzzle:

2014-03 Level 4 Answer

The chart below shows one possible way to arrive logically at the solution.

2014-03 L4 steps

49 and V is for Victory Puzzle

49 is a composite number, and it is 7 squared. 49 = 1 x 49 or 7 x 7. Factors of 49: 1, 7, 49. Prime factorization: 49 = 7 x 7 which can also be written 49 = 7².

Since √49 = 7, a whole number, 49 is a perfect square. 

Whenever 49 is a clue in the FIND THE FACTOR puzzles, write 7 in both the corresponding factor column and factor row.

Level 3 is the first level of the higher level FIND THE FACTORS puzzles. For many people going from level 2 to level 4 would be too overwhelming. Level 3 is a bridge between those two levels and allows a person to move on from the lower levels and victoriously solve a little more difficult puzzle. V is for that victory.

Level 3 puzzles are designed to be solved starting from a row or column at the top of the puzzle with 2 clues. First find the common factor of those two clues that will allow you to write only numbers from 1 to 10 in the first column of the puzzle. Then factor row by row to the bottom of the puzzle making sure each number from 1 to 12 is written only once in both the factor row and the factor column. You will notice a rhythm for the answers as you work.

2014-04 Level 3

 

This week’s puzzles are available in an excel file here. If you have a spreadsheet program on your computer, you can access it. If you enable editing in excel, you can type your answers directly onto the puzzle, and you can also easily print the puzzles. May you be victorious in your efforts!

Here are the factors to last week’s level 3 puzzle:

2014-03 Level 3 Answer

 

This puzzle was solved starting with the column with 2 clues near the top of the puzzle and then factoring row by row until we reached the bottom of the puzzle.

48 and What’s wrong with this?

48 is a composite number. 48 = 1 x 48, 2 x 24, 3 x 16, 4 x 12, or 6 x 8. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. Prime factorization: 48 = 2 x 2 x 2 x 2 x 3, which can also be written 48 = 2⁴ x 3.

Sometimes 48 is a clue in the FIND THE FACTORS puzzles. Even though it has many other factors, we use only 6 x 8 for the FIND THE FACTORS 1-10 puzzles and 6 x 8 or 4 x 12 for the FIND THE FACTORS 1-12 puzzles.

 

factor tree

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Below is some fabulous mathematical slight of hand.  Something is wrong with it, but what?

The Science Magician - Dr Matt Pritchard

Image

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47 and Understanding the Equal Sign with Candy

47 is a prime number. 47 = 1 x 47. Its only factors are 1 and 47. Prime factorization: none.

How do we know that 47 is a prime number? The square root of 47 is an irrational number approximately equal to 6.86. If 47 were not a prime number, then it would be divisible by at least one prime number less than or equal to 6.86. Since 47 is not divisible by 2, 3, or 5, it is a prime number.

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

What a wonderful lesson! Teachers or parents can easily follow Jen’s lesson plan. I’m certain children will always remember what an equal sign means forever after. (It will be necessary to click twice to get to the lesson.)

Beyond Traditional Math

I am so thrilled to be guest posting today over at Minds in Bloom, Rachel Lynette’s awesome blog! In the post I talk about how I noticed a misconception that my students had about the equal sign.  I decided to use candy to help my students understand what the equal sign *really* means.

Click the image below to read on!

Screen Shot 2014-01-18 at 9.11.13 PM

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