## Suma Gakuen past problems

arithmetic

As shown in the figure, black stones and white stones are arranged alternately and regularly one by one.

1st stage ●

2nd stage ○○○

3rd stage ●●●●●

4th stage ○○○○○○○

(1) How many stones will be in total when arranging up to the 8th row?

(2) What is the difference in the number of black stones and white stones when arranging up to the 10th row?

(3) The difference in the number of black stones and white stones is 66 when they are lined up.

Arithmetic answer

(1) 64 pieces, (2) 10 pieces, (3) 66th stage

<Explanation>

## (1) 1 + 2 x (8-1) = 15 (1 + 15) x 8 ÷ 2 = 64

##

## (2) 1 + 4 x (10-1) = 37 (1 + 37) x 10 ÷ 2 = 190

## 3 + 4 x (10-1) = 39 (1 + 39) x 10 ÷ 2 = 200 200-190 = 10

##

## (3) At the first stage, the difference is 1. At the second stage, the difference is 2 ...

## Therefore, the difference that can be made when one step is increased is one.

## Therefore, when the difference is 66, it is when the 66th row is lined up.

##

Science

Substances that have the function of decomposing starch and proteins are called digestive enzymes.

Select one of the digestive enzymes contained in the solution from the following (1) to (4) and answer with a symbol.

① Peptidase ② Lipase ③ Pepsin ④ Amylase

Science answer

national language

Choose one word each that is most relevant to the content of the following proverb and answer by number.

A. A talented hawk hides its claws.

1. 1. Failure 2. Effect 3. Objective 4. Ichizu 5. Cooperation 6. Humility

7. 7. Experience 8. Beware

Japanese answer

A.6 B.1 C.3 D.7 O.8

society

## What is the method of transporting what was carried directly to the destination by car in relation to limited express trains and high-speed buses, in combination with cars and railroads in order to reduce exhaust gas? Answer in katakana.

Social answer