Perfect Practice Makes Perfect

# Code

## Tuesday’s Twister #13 – Prime Numbers

May 19th, 2015 by John Lehet

“There are three kinds of people: Those that make things happen, those that watch things happen and those that wonder what happened. ” – Agent Garbo (Juan Pujol Garcia)

Prime numbers are everywhere and they are really easy to understand.  There are just two simple rules to follow:

• – a prime number is a positive integer greater than 1
• – a prime number is evenly divisible by only 1 and itself

That’s pretty straight forward.  Many people assume 1 is a prime number, but by definition, it’s not.  It’s important to realize and remember this when dealing with primes.  Also, 2 is the only even prime number, as all other even numbers are divisible by 1, 2 and itself.

Here’s a couple of prime number puzzles to start you off.

puzzle 1: What is the smallest 2-digit prime number in which both digits are prime and their sum is prime?

puzzle 2: What is the largest 2-digit number in which both digits are prime and their sum is prime?

Let’s look at an example number, say 73.  73 is a prime number and it’s digits, 7 and 3 are both  prime.  However, the sum of the digits 7+3 equals 10, which is not prime.  So, 73 will not work for either puzzle 1 or puzzle 2.

Once you solve the first two puzzles, you should have a good handle on prime numbers.  I recommend listing all of the prime numbers less than 100.  To make it a bit more challenging, let’s look at 3-digit numbers.

puzzle 3: List all 3-digit numbers that have prime numbers for all three digits.

puzzle 4: Of the numbers listed in puzzle 3, list the numbers in which the digits sum to a prime number.

puzzle 5: Of the numbers listed in puzzle 4, which of the numbers are themsleves prime?

Let’s look at an example 3-digit number, say 235.  the digits, 2, 3 and 5, are all prime numbers.  However their sum, 2+3+5, equals 10, which is not a prime number (so it doesn’t work for puzzle 4).

Good luck with the puzzles and have fun.

## 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!

## Tuesday’s Twister #7 – More Hex Codes

February 17th, 2015 by John Lehet

Some of us think that holding on makes us strong, but sometimes it is letting go.” – Hermann Hesse

Today’s puzzles are Hex Codes.  I introduced some Hex Codes during the Holiday Puzzles back in December. Each puzzle is a collection of adjacent hexagons that follow a pattern.  In today’s puzzles, each hexagon contains either a number or is empty.  The objective is for you to fill in empty hexagons with the correct number that follows the given pattern.  You must determine the pattern that each puzzle exhibits in order to correctly complete each puzzle.  The hexagons may vary in color which may be of importance (hint, hint, nudge, nudge).  Some of the puzzles may use addition or subtraction, while others may utilize some other connection (like adjacent hexagons or the color) between certain attributes.  That’s all for you to figure out.

Below are two Hex Code puzzles for you to try.  All you need to do is to figure out the pattern in each puzzle and then use it to fill in the empty hexagons.  The puzzles are different codes so the colors have different meaning within each puzzle.  Best of luck!

Puzzle 1

Puzzle 2

As always, I hope you enjoyed these puzzles.  Please pass them onto others who may enjoy them and please click LIKE below if you like them!

## Holiday Puzzle #24 – Rebus Puzzles

December 24th, 2014 by John Lehet

Continuous effort – not strength or intelligence – is the key to unlocking our potential.” – Winston Churchill

Today we end the 2014 Holiday Puzzles with Rebus Puzzles.  These are puzzles that can be enjoyed by nearly everyone, young and old alike.  Some are original, but most of them have been borrowed.  Regardless of their origin, they are fun and challenging.  I’ve assembled 12 rebus puzzles below – some easy and some a bit more challenging.

For those that have never done a Rebus puzzle, each puzzle cryptically equates to a saying or a word.  Your objective is to try to determine what word or phrase is meant.

Good Luck and pass the puzzles onto others who may enjoy them!  I hope everyone enjoyed the puzzles – please select Like below or send me an email with comments!

## Holiday Puzzle #23 – Number Circuits

December 23rd, 2014 by John Lehet

Magic is believing in yourself. If you can do that, you can make anything happen.” – Johann Wolfgang von Goethe

Today’s puzzle is an original puzzle – Number Circuits.  Initially I named these puzzles Magic Puzzles.  However, when Mindware agreed to publish the puzzles, I agreed to change the name.  I currently have two books of different levels of difficulty available, conveniently named Number Circuits Level A (easier) and Number Circuits Level B (harder), both of which are available on Mindware.  As with many puzzles, the concept is very straight-forward and getting an answer is very easy, but getting the correct answer is a bit more challenging.

Below is an interactive puzzle sampler with six puzzles.  These are drag-and-drop puzzles in which you can select a number in a yellow circle (left click and hold) and drag to an empty circle (move the mouse and release left click).  The number should “snap” to the nearest empty circle (assuming it’s close enough).   Each puzzle contains directions and there is a general help button that provides further information.  Good luck!   Click here to request a pdf version of the puzzle.

Good Luck and pass the puzzles onto others who may enjoy them! Tomorrow, Wednesday the 24th, will be the last day of my Holiday Puzzles.  I promise it will be a fun puzzle that everyone will be able to try!

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

## Holiday Puzzle #10 – Hex Codes

December 10th, 2014 by John Lehet

Do not let what you cannot do interfere with what you can do.” – John Wooden

Today’s puzzles are Hex Codes.  Each puzzle is a collection of adjacent hexagons that follow a pattern.  Each hexagon contains either a number/letter or is empty.  The objective is for you to fill in empty hexagons with the correct number/letter that follows the given pattern.  You must determine the pattern that each puzzle exhibits in order to correctly complete each puzzles.  The hexagons may vary in color which may be of importance (hint, hint, nudge, nudge).  Some of the puzzles may use addition or subtraction, while others may utilize some other connection (like adjacent hexagons or the color) between certain attributes.  That’s all for you to figure out.

So all you need to do is to figure out the pattern in each puzzle and then use it fill in empty hexagons.  Best of luck!

As always, I hope you enjoyed these puzzles.  Please pass them onto others who may enjoy them!