Number Sense

“It is the brain, the little gray cells on which one must rely” – Hercule Poirot

Today’s puzzle is a great puzzle that everyone can enjoy.  They are called alphametics.  In each puzzle, there is a simple arithmetic problem.  However, instead of using numbers, letters are used.  Each letter stands for a single digit number (e.g. 0,1,2,3,4,5,6,7,8 or 9).   Within each puzzle, a number can be associated with only one letter, so two different letters can not equal the same number.  The meaning of the letters may change from puzzle to puzzle, so “N” may be “5” in the first puzzle and may be “3” in the second puzzle.  The objective is to assign each letter a number so the statement is correct.  It sounds straight-forward and is easy to understand, but may be very challenging.  Here’s an example:   

Make sure you understand the example. When you do, try the following puzzles. Good Luck!

I hope you enjoyed the puzzles.  Please pass the puzzles onto others who may enjoy them!

“He who wonders discovers that this in itself is a wonder” – M. C. Escher

Today’s puzzle is an original puzzle which I believe to be very challenging. I call them Self-Referential Puzzles. They are similar to the Number Sense Puzzles (from yesterday) in that you are given a statement for which you find a number. The difference is that in Self-Referential Puzzles, the statement refers to the statements in the puzzles. What’s that mean? Well, in Number Sense Puzzles, statements were something like “Number of quarts in a gallon” which is always 4 (it never changes). In Self-Referential Puzzles, the statement may be something like “The number of even number solutions”. Well this is all together different because when a solution is changed it may impact and change some or even all of the other solutions. 

So, the important thing to remember is that when you enter or change a number in the puzzle it is very likely to effect other numbers.  In turn, the other numbers may change which will likely effect other numbers.  And this goes on and on! That’s the beauty of the puzzle – changing one answer may change all of the answers!

I’ve put together an interactice “drag and drop” puzzle sampler that has six different self-referential puzzles.  As always with my interactive puzzles, you will need to be able to access Adobe Flash.  Each puzzle has it’s own set of directions and numbers that can be used.

“Look at the stars and not down at your feet. Try to make sense of what you see, and wonder what makes the universe exist. Be curious.” – Stephen Hawking

Here’s a new type of puzzle that I call Number Sense Puzzles.  They are geared for younger puzzlers to help them improve their number sense.  There will be 8 statements each corresponding to a number.  You have to use the numbers 0 through 9 once and only once to fill in the correct number for each statement.  You will need to use and develop your deductive problem solving skills in order to correctly place the numbers.  Since there are only 8 answers and 10 numbers (0 through 9), some of the answers will require two digits. 

I created an interactive puzzle that will automatically check your answer and provide feedback. I also created a pdf file that can be used in classrooms or with pencils for those so inclined. The goal is to have fun and challenge yourself.

I hope you enjoy these puzzles.  If you find these interesting, Click Here for a selection of more Number Sense puzzles that I’ve created.  I will be adding to the selection over time. Good Luck and pass the puzzles onto others who may enjoy them!

“Even if you fall on your face, you are still moving forward.” – Victor Kiam

Here’s a new original puzzle that is another great challenge for everyone. It emphasizes combining even numbers (2,4,6 and 8) with addition, subtraction, multiplication and division using the rules of order of operations.

The rules are simple:

1. Use only the numbers 2, 4, 6 and 8
2. Use each number once and only once
3. Use any of + – x / to combine the numbers
4. Use parenthesis () as desired
5. Following rules 1-4, make the numbers 0-9

For example, “11” can be made as “(8 + 6) / 2 + 4″. In this example, each number (2,4,6,8) was used once and only once as required. There are other ways to make “11” which would also work.

I put together a little interactive program for this puzzle. You can enter your answers for each number and then select check. Your answers will be scored and a response provided (e.g. “got it!” or “need to use 2,4,6 and 8″). Give it a try and let me know what you think.  Click here for a pdf file.

I hope you enjoy this puzzle.  Good uck and pass it onto others who may enjoy them!

In order to use the interactive puzzle, you need to have adobe flash enabled.

“What people don’t realize is that professionals are sensational because of fundamentals” – Barry Larkin

Number sense if a fundamental skill.  I like to refer to it as “Number Familiarity“. How familiar are are you with numbers.  For example, take the number 64.  How familiar are you with the number 64?  

• – Do you know it’s a perfect square?    
  – Do you know it’s a power of 2?    
  – Do you know it’s a perfect cube?  
  – Do you know it’s the product of two perfect squares?
  

64 equals all of these – it’s 8²,   2⁶,   4³  and   (2²)(4²). 

I think that simply stated number puzzles are a great way to increase number sense.  It doesn’t matter if you’re seven or eighty-seven, concise number puzzles can be beneficial.  Here’s a few concise number puzzles to try:

1. Can you think of two numbers that when multiplied make 8 and when added make 6?
2. Can you think of two numbers that when multiplied make 32 and when added make 18?
3. Can you think of two numbers that when multiplied make 48 and when added make 14?

These puzzles should not be solved algebraically (e.g. via a system of equations).  Instead, these puzzles should stimulate thinking and making number connections.  They should also generate confidence.  There are very few things that generate confidence better than success.  Once these puzzles are mastered, change it up a bit.  Keep the puzzles generally the same, but ask for something different.  Instead of asking for the numbers, ask for the difference of the numbers, or ask for the smaller or larger number.  This adds another level of challenge to the problem.  Here are a few additional number puzzles to try:

1. What is the difference of two numbers that when multiplied make 18 and when added make 9?
2. What is the larger number of two numbers that when multiplied make 30 and when added make 13?
3. What is the smaller number of two numbers that when multiplied make 48 and when added make 19?

These puzzles are similar to the first set of puzzles, but differ as they are more challenging because the two numbers must be further manipulated to obtain the correct answer.  Continuing this theme of making the puzzles more challenging, here are a few more number puzzles to try:

1. Can you think of two numbers that when multiplied make 16 and adding one number to twice the other makes 8?
2. Can you think of two numbers that when multiplied make 24 and adding one number to twice the other makes 14?
3. Can you think of two numbers that when multiplied make 36 and adding one number to three times the other makes 21?

These puzzles will help build fundamental number sense.  They can be easily stated, understood and quickly solved.  They serve as great 1-minute problems and can assist in building confidence which will lead to even better problem solving skills.  Give them a try and share them if you like them.  Have fun and good luck!