Math New Drill (Level 1) : Number of cases Point moving on the side of a square

There is a square ABCD whose length of one side of is 1. 

First, the point P is in the position of A. 

When I throw one coin and head comes out, the point P moves 1 and tail comes out, P moves 2 in the direction of an arrow on the side. 

When I throw coin 5 times, the point P came to the position of A. 

In this case, how many kinds of way of head and tail coming out are there? 

<Example> When throwing twice and coming to the position of D, there are two kinds, (Head, Tail),(Tail, Head).

Math New Drill (Level 2) : Number of cases Ways of route for moving

Answer the following questions. 

(1) How many ways of route from A to B is there in lower Fig. 1? 

Noted that there are right or down directions of moving. 

(2) How many ways of route from A to B is there in lower Fig. 2? 

Noted that there are right or down or lower right directions of moving. 

(3) How many ways of route from A to B with passing along neither P nor Q is there in lower Fig. 3? 

Noted that there are right or down or lower right directions of moving.

Math New Drill (level 1) : Number of cases Problem 2(5) TOYOEIWA-2008

How many ways of method of putting two oranges and two apples on three plates of white, green and blue are there? 

Noted that there shall be no empty plate.

Math New Drill (level 2) : Number of cases SNJ00-0807-L2 Two types of road to move forward

There is a road shown in the figure below. 

I can move forward on the road expressed by the solid line at a speed of 2 times more than the road expressed by the dotted line. 

How many ways of method to go from A to B in fastest time are there?

Math New Drill (Level 1) : Number of cases Connect five points

The figure below is a diagram with a number of 1-5 at the apex of the symmetrical pentagon (not a regular pentagon).

Drawing a straight line starting from 1 and go along each point from 2 to 5 only once and return to 1. 

How many kinds of figure are made? 

The figure that can be overlapped is considered to be the same figure.

Math New Drill (Level 1) : Single stroke drawing

This figure is drawn with a single stroke of the brush. 

How many ways of drawing are there in all?

Math New Drill (Level 2) : Triangles on a circle

There are eight points on the circumference at equal interval.
A triangle is made by choosing three points among eight.
How many kinds of triangle are made?

Math New Drill (Level 2) : Number of cases Moving insect

As shown in the figure below, nine points are at the vertex of the four squares. 

An insect leaves A and moves to the next point every second. 

How many ways of moving the insect is at B 6 seconds later are there? 

It can pass points and sides more than twice.

Math New Drill (Level 2) : Number of cases Cut one paper into three pieces

There is a rectangular paper on which square grids are drawn. 

This paper is cut twice straight along the grid. 

When it's a paper in the figure below, you can make 3 kinds of figure. 

(1) When cutting the rectangular paper below twice, how many kinds of figure can you make? 

(2) When it's cut once again, how many kinds of figure can you make?

Math New Drill (Level 2) : SNJ00-0807-L2 Cut one paper into three pieces

There is a rectangular paper on which square grids are drawn. 

This paper is cut twice straight along the grid. 

When it's a paper in the figure below, you can make 3 kinds of figure. 

(1) When cutting the rectangular paper below twice, how many kinds of figure can you make? 

(2) When it's cut once again, how many kinds of figure can you make?

New Math Problem (Level 1) : Number of cases Problem 2 OTSUMA-2014

Five parts in the figure below are painted by three colors of red, white, and yellow. 

How many ways of painting are there in all? 

Noted that any part should be painted in a different color from the next part.

New Math Drill (Level 1) : SNJ00-0804-L1 Product of three numbers is 24

There are three boxes of red, yellow and blue. 

Nine cards of the color same as the box which numbers from 1 to 9 were written are in the each box. 

One card is taken out of each box. 

How many ways of taking out are there in total that the product of three numbers becomes 24?

New Math Drill (Level2) : SNJ00-0806-L2 Moving on straight or circle road

There is a road such as in the figure below.



How many ways to go from A point to O point with obeying the following rules of advance are there?

(Rule 1) You may return to the intersection where you passed once, but you may not pass the road twice.

(Rule 2) You may not advance on the straight road towards the direction which you back away from O point.

Math New Drill (Level 1) : Number of cases Problem1(4) JOSAIKAWAGOE-2014

There are four balls of red, blue, yellow, green and four boxes of red, blue, yellow. 

How many ways to put each ball in each box so that it may be different from the color of the ball and the box are there?

New Math Drill : Level 1 : Number of cases Problem2(5) JISSENJOSHIGAKUEN-2014

There are five sheets of cards of 0, 1, 1, 2, 3. 

I take out two sheets out of five and make two digits of integers. 

How many different integers are there in all?

Math New Drill : Level 2 : SNJ00-0807-L2 Number of triangle with three points inside

As shown in the figure, 19 points are arranged regularly. 
Make a triangle by connecting three points from these points. 

Noted that three sides of triangle do not pass through any other points except vertexes of the triangle. 

How many triangles containing three points inside are there in all?

Math New Drill : SNJ00-0802-L1 Two sheets of cards with same number

How many kinds of integers can be made by arranging three cards among six cards of 1, 2, 2, 3, 4, 5?

Math New Drill : SNJ00-0806-L2 Number of directions turning three times

There is a road as shown in the figure below. 
Travels the shortest distance from A to B. 
How many ways of turning at a corner 3 times are there?

Math New Drill : Level 2 SNJ00-0812-L2 Election of representative of the class

3 people of Taro, Jiro, and Hanako ran for the election of one representative in a class. 

There are 45 students in this class. 

Every student voted one with the name of one person. 

The table below shows the number of votes of three when 20 votes are counted. 

How many more votes does Hanako need to win certainly?

Math New Drill : Level 2 SNJ00-0804-L2 Put 10 balls into 5 boxes

How many ways are there putting two red balls, two black balls, and six white balls into five different boxes by two in each box? 
Same color balls cannot not be distinguished.