Perfect Practice Makes Perfect

# number puzzles

## Holiday Puzzle 2015 #10 – Snowflake Puzzles

December 10th, 2015 by John Lehet

“Begin doing what you want to do now. We are not living in eternity. We have only this moment, sparkling like a star in our hand and melting like a snowflake.” – Francis Bacon

Today’s puzzle is called a Snowflake Puzzle.  This is an extension of the Kuruko Puzzles that I created. Like Kurulko puzzles, they are similar to Sudoku puzzles.  I call them Snowflake puzzles because of their shape.  Snowflakes are symmetric shapes with six points.   The Snowflake puzzle follows this design.  It is comprised of 42 hexagons (six sided shapes).  There are white and yellow hexagons.  To complete the puzzle you must fill in each of the empty white hexagons.  There are two simple rules to follow:

1. Surrounding each yellow hexagon there are six white hexagons, these must contain the numbers 1 through 6 (each number once and only once)

2. The number in each yellow hexagon is the sum of the numbers in the three white hexagons that point to it (with a black triangle).

Here’s a snowflake puzzle for you to try –   Click here for a pdf file.

If you like the snowflake puzzle, take a look at the book of 100 Kuruko Puzzles that I wrote which is available on Amazon.com.  Good Luck and pass the puzzles onto others who may enjoy them!

## Tuesday’s Twister #19 – Number Circuit Puzzles

November 3rd, 2015 by John Lehet

In November and December each year I make classroom presentations for elementary schools. One of my presentations is on Problem Solving. I am a big believer that puzzles are a great way to introduce and improve problem solving skills. I use my original Number Circuit puzzles. I have developed a complete Lesson Plan and Teacher’s Guide to complement my presentation. I essentially break problem solving down into five steps:

2. What Do I Know? (a question all problem solvers should ask)
3. What Am I Looking For? (another question that must be answered)
4. What Can I Conclude? (This is the tough one!)
5. Solve The Problem

Too often I see children jump right to step 5 and try to solve the puzzle (or problem) without doing all or even any of the preliminary steps. Although skipping steps is sometimes faster, it is all too often unsuccessful. Go Fast Slowly is what I tell them. Take your time. Speed is not important. However, getting the correct answer and improving are both REALLY important! Please take a look at the supporting materials and give the puzzles a try. Remember it’s about having fun and getting better at the same time!

click here for the Teacher’s Guide to Problem Solving with Number Circuit Puzzles
or

Below is a collection of six interactive Number Circuit puzzles for you to try!

I hope you enjoy these puzzles. If you find these interesting, Click Here to view our complete collection of puzzle books. Good Luck and pass the puzzles onto others who may enjoy them!

## Tuesday’s Twister #12 – Sequences

May 13th, 2015 by John Lehet

“Lost time is never found again.” – Ben Franklin

When working with students in elementary school, I like to talk about sequences or number patterns.  I often present them with the start of a sequence, say the first three numbers.   I then ask the class to give me the next term (or number) in the sequence.  Letting everyone in the class mull it over for a bit, I ask for the pattern (the code essentially) and the next few numbers.  When I first did this, I was amazed!  I had a sequence in mind, but the students kept giving different, yet very viable sequences.  Not only that, they could justify their answers by supplying the “code” for the sequence.  I quickly realized that with just three numbers at the start of a sequence, the possibilities were plentiful.  It was quite the challenge for the students also.

So, I started doing this as a “break the ice” activity with classrooms.  We would use the same three numbers again and again, and see how many different (yet viable) sequences could be made.  When they give me a sequence and its corresponding justification, I would say “great, let’s find another” and erase it leaving only the first three “seed numbers” that I had originally written.  I  would then ask them to give me another different sequence and the whole thing would start over again.  Each time I do this, I am still amazed at how many different sequences they come up with and how challenging they find it.  Here’s the start of a sequence for you to try …

## Here’s three numbers that start a sequence:    2, 3, 5, . . .

What do you think the next number can be?  How about the number after that?  Remember, it has to follow a pattern, so you can easily find each successive number by applying the pattern.

I’ve given this pattern to numerous classrooms.  Each time,  they came up with a variety of different answers, all of which make a valid sequence.  For the next number, classes have given 7,  some have given 8 while others have given 14.  In all, from all of the classes, I have received 9 different sequences that these three numbers can generate (and there’s even more!).

My challenge to you is to find as many different sequences that can be generated using the first three numbers  2, 3, 5.  Remember don’t just come up with the sequence, but identify the pattern that it follows.  Challenge yourself to see if you can find nine different sequences.  Good luck, have fun and challenge others, the more the merrier!