Jayadratha (जयद्रथ), the envious tyrant of Sindhu, was reclining on his fifteen pillows, trying to get comfortable – and failing. He suddenly realized the reason… The stacks of pillows needed to decrease in height from left to right. This was easy…

Yes! Jayadratha (जयद्रथ), the envious tyrant of Sindhu, figured out a perfect way to position all 15 pillows. However no sooner had he done this and began to get comfortable in his superiority when an avatar (we’ll keep his name mysteriously secret) disturbed his peace… 

The avatar challenged Jayadratha… “I can make a superior pile of pillows…”

The avatar showed Jayadratha (जयद्रथ), the envious tyrant of Sindhu, his alternate arrangement of the fifteen pillows.

“No!” said Jayadratha, they need to all be different in height. Your stacks are all the same height.

The avatar was not put off, but tried again…

“No!” said Jayadratha, they are of different heights, but they need to decrease in height from left to right. Your stack # 2 is shorter than stack #1.

The avatar was not put off, but tried again…

“Ahhh!” said Jayadratha… Your stack #1 is higher than mine (1 point for you). Your stack #2 is higher than mine (1 point for you). Your stack #3 is higher than mine (1 point for you). My stack #4 is higher than your zero height stack (1 point for me). My stack #5 is higher than your zero height stack (1 point for me).

“That means you win” cried Jayadratha “but because I’m the stronger, I’ll steal your design.”

The avatar didn’t give up. He tried {6,5,2,1} to beat Jayadratha’s {6,5,4}.

“No!” snickered Jayadratha, In stacks #1 we tie, in stacks #2 we tie, in stack #3 I win(one point for me) and in stack #4 you win (one point for you)… So you have not beaten me… only tied me. And I’m adding one last rule. If you tie on any stack your challenge automatically fails. Here we are tied on stack #1, so you automatically fail.

The avatar didn’t give up. He tried {8,7} to beat Jayadratha’s {6,5,4}.

“You win!” wailed Jayadratha. You get two points for beating me in stacks #1 and #2. I only get 1 point (stack #3.)

But I will again steal your design and finally get some sleep…

But the avatar did not give up. Instead he quickly built the original stack. {5,4,3,2,1} beats {8,7}.

How does the story end? Can Jayadratha find an stackable arrangement of 15 pillows that cannot be beaten by the avatar? The answer is yes. Do not go onto the next slide until you or your class has solved this.

I believe there are just three solutions.

The mathematical thinkers among your children should be asking themselves: will the avatar or Jayadratha win for different numbers of pillows. Start out simply. One pillow, two pillows, three pillows…

There something special about this problem between 20 and 30, but this is not where you would want to start your exploration of this problem. That’s all I’ll say. Enjoy!

Puppet Puzzle

(MathPickle, 2016)

I use puppet puzzle with large blocks that I can recline on. The students try to find a way to beat me. Every time they do, I play the evil tyrant and seize their design.

Here is a pdf of the presentation.

Puppet images thanks to Tropenmuseum, Amsterdam.

Standards for Mathematical Practice

MathPickle puzzle and game designs engage a wide spectrum of student abilities while targeting the following Standards for Mathematical Practice:

MP1 Toughen up!

Students develop grit and resiliency in the face of nasty, thorny problems. It is the most sought after skill for our students.

MP2 Think abstractly!

Students take problems and reformat them mathematically. This is helpful because mathematics lets them use powerful operations like addition.

MP3 Work together!

Students discuss their strategies to collaboratively solve a problem and identify missteps in a failed solution. MathPickle recommends pairing up students for all its puzzles.

MP4 Model reality!

Students create a model that mimics the real world. Discoveries made by manipulating the model often hint at something in the real world.

MP5 Know the tools.

Students master the tools at their fingertips - whether it's a pencil or an online app. 

MP6 Be precise!

Students learn to communicate using precise terminology. MathPickle encourages students not only to use the precise terms of others, but to invent and rigorously define their own terms.

MP7 Be observant!

Students learn to identify patterns. This is one of the things that the human brain does very well. We sometimes even identify patterns that don't really exist 😉

MP8 Be lazy!?!

Students learn to seek for shortcuts. Why would you want to add the numbers one through a hundred if you can find an easier way to do it?


Please use MathPickle in your classrooms. If you have improvements to make, please contact me. I'll give you credit and kudos 😉 For a free poster of MathPickle's ideas on elementary math education go here.

Gordon Hamilton

(MMath, PhD)