# For junior high and high school students

Let's make a new problem to discover new things.!

I am Higeo. Do you want to discover new things or new formula in math, and leave some things in the history of mankind?

My friends Pyon and Penta were wondering how they discover new things.

Therefore, I came here to teach them how to discover new things and formulas in mathematics.

## How to make a new formula.

Higeo

If you want to make a new formula, you need make a new problem.

Pyon

There are many problem books in the library, but how can I make a new problem?

Penta

Is it possible to make a new one? No! It is too difficult.

Higeo

It is very difficult to make a new problem from nothing. We need a certain matetial with which we make new problem.

Pyon

Material?

Higeo

Some problem by which we can make a new one. Our method is to make a new one by chaning some parts of the original one.

## Let's look for some interesting problems.

Penta

Please introduce some good problem to me.

Higeo

Wait a minute.

We use Wasabi. It is similar in taste to hot mustard. There are ten Sushi, and three of them contains a lot of Wasabi. They are impossible to eat. Two players A and B take turns, and eat one of them. They do not know which of Susi contains Wasabi The player who eats the Susi with Wasabi is the loser of the game.

Oh! This is a Russian roulette of Susi!

Penta

Sound interesting!

## To make a variant.

### To change numbers.

Higeo

How can we change the problem?

Penta Pyon

Wait a minute.

Penta

Perhaps, it is more fun to do this with more than two persons.

Pyon

What do yo mean?

Penta

Perhaps we can do this with 100 persons instead of two.

Pyon

Perhaps we can do this with more number of Susi.

Penta

Perhaps we can play this game more number of Susi with Wasabi, and that will make the game more exciting.

Higeo

What you proposed to do are good way to change a problem. Perhaps it was not difficult to change some parts of problem for you.

### To change the rule

Penta

Is there any other way to change problem?

Pyon

When you eat one Susi with Wasabi, the game ends. This rule seems to be too simple.

Penta

Then, we can change the rule. When you eat two Susi with Wasabi, you lose in the game. Perhaps this rule is better.

Pyon

How about this rule? The player who eats the last Susi with Wasabi loses in the game.

Penta

How about a player's winning the game when he or she eats Susi with wasabi?

Pyon

Is there any way to change the rule more dramatically?

Higeo

How about changing the rule "take turns"?

Pyon

A different order of eating Susi!

Penta

The order of eating for A and B can be "AAAB...".

Pyon

Is it very unfair?

Higeo

Then, what is the fair oder for each player?

Penta Pyon

What do yo mean?

Higeo

If players A and B take turns, then the chance of getting Susi with Wasabi is bigger for A.

Penta Pyon

Really?

In this way, by changing some parts of the original problem, you can have a new perspective on the problem. Then, you get a new problem to solve.

Then, you are going to discover new formulas and new facts of mathematics.

In fact, we tried to find an order by which two players A and B have the same chance of losing in the game, and we discovered a new formula.

In this way, it is not difficult to discover new things. What you have to do is to change some parts of the original problem, and study the variant that you make.

## Appendix

Higeo

Perhaps some one is still think it impossible for him or her to do research.

Pyon

Please do not give up.

Penta

If you think math is not for you, then please watch movies made by one of our group. Higeo, Pyon and Penta are the main characters of this animation movie. These movies have got some prizes in movies contests.

Higeo

We also used our way of creating new things in these movies, too.

Pyon

Please watch them!

Higeo

These movies are on the last part of Gallery in our website.