Science Trivia Resume

There are 9 coins and one of them is fake which is lighter than the others. Find a fake coin using balance (with no scale and weight) 2 times

△ ABC is a right-angled triangle whose ∠ A = 90 degree. The area of square Y + Z = X (Pythagorean theorem)  Then, when you cut off square X and make Y, Z of pieces of X, show the lines you cut.    

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?

In integers from 1 to 3000, find the number of figures that do not use number 7.

Find the remainder when the number of the 100th power of 123 is divided by 11.

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. 

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?

This figure is drawn with a single stroke of the brush.  How many ways of drawing are there in all?

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.

If the cube is cut along with the bold line, which is the right development view from ① to ⑧?

A square card below is cut along the dotted line. It is divided into two pieces where both of shape and the size are same . Answer six ways of cutting. When it is rotated or turned over and it becomes the same, it is assumed to be one way. 

A square card below is cut along the dotted line. It is divided into four pieces where both of shape and the size are same . Answer six ways of cutting. When it is rotated or turned over and it becomes the same, it is assumed to be one way. 

A rectangular card below is cut along the dotted line. It is divided into two pieces where both of shape and the size are same . Answer five ways of cutting. When it is turned over and it becomes the same, it is assumed to be one way. 

6 kinds of animals are drawn by two in a single card. The card is divided into two pieces where both of shape and size are same by cutting it along the dotted line. It should be cut so that 6 kinds of animals may belong to each piece by one. Answer four ways of cutting.

6 kinds of animals are drawn by two in a single card. The card is divided into two pieces where both of shape and size are same by cutting it along the dotted line. It should be cut so that 6 kinds of animals may belong to each piece by one. Answer how it is cut.

4 kinds of animals are drawn by two in a single card. The card is divided into two pieces where both of shape and size are same by cutting it along the dotted line. It should be cut so that 4 kinds of animals may belong to each piece by one. Answer how it is cut.

  Make a figure below by combining five pieces of block above.

There is a flower with 13 petals as shown in the figure below.   2 people decide an order to take petal.  One petal or two petals adjacent for once are taken in turn.  There is a legend that fortune visits for the person who takes the last petal.  When you do this floral fortune-telling with somebody, do you choose the first taker or the second taker in your turn?

By cutting twice the figure below with scissors, make one square of the same area as this figure.