Cause Granny has 10 grandchildren and all of them have a different ages so 

I call the ages of ten children are \(x_1,x_2,....,x_{10}\)

Cause Alice is the eldest 

We have \(x_1+x_2+....+x_{10}=180\)

=> \(10x_{10}\ge180\)       

<=>  \(x_{10}\ge18\)

So , at least , the age of alice is 10 

2 perfects squares: 1 and 4

Lê Anh Duy Oh I forgot :)

what about 9?

a) I don't know

b)3:9:81::5:25:125

Answer: Just 2 times of weight: First time: Divide 9 coins into 3 parts, each with 3 coins (3; 3; 3). Place the first and the second parts on the scale, if somewhat lighter, the part contains counterfeit copper, if these two parts are equal, the counterfeit is in the third part.

2nd time: After the 1st weighting above, the part containing the fake copper was identified. This part has 3 coins, of which only 1 fake. Put any 2 coins on two weighing plates, if the dong is lighter then that is a fake, if the two coins are equal, the other is a fake.

- If a + b + c \(\ne\)0 then

\(\dfrac{2a}{b+c}=\dfrac{2b}{a+c}=\dfrac{2c}{a+b}=\dfrac{2a+2b+2c}{b+c+a+c+a+b}=\dfrac{2a+2b+2c}{2a+2b+2c}=1\)

=> \(m=1\)

- If a + b + c = 0 then

b + c = -a

a + c = -b

a + b = -c

=> \(\dfrac{2a}{b+c}=\dfrac{2b}{a+b}=\dfrac{2c}{a+b}=\dfrac{2a}{-a}=\dfrac{2b}{-b}=\dfrac{2c}{-c}=-2\)

=> \(m=-2\)

- If a + b + c ≠

0 then

2ab+c=2ba+c=2ca+b=2a+2b+2cb+c+a+c+a+b=2a+2b+2c2a+2b+2c=1

=> m=1

- If a + b + c = 0 then

b + c = -a

a + c = -b

a + b = -c

=> 2ab+c=2ba+b=2ca+b=2a−a=2b−b=2c−c=−2

=> m=−2

The kilograms of rice left after the 2nd day sold is:

30 + 1/3 = 91/3(kg)

The kilograms of rice the store have at first is:

91/3 + 2/3 = 31(kg)

Answer: 31 kg

The kilograms of rice left after the 2nd day sold is:        

                 30 + 1/3 = 91/3 (kg)

The kilograms of rice the store have at first is:

                  91/3 + 2/3 = 31 (kg)

                           Answer: 31 kg of rice 

Lượng gạo đầu tiên của cửa hàng là 31 kg

Mai has notebooks number is :

                3 + 4 = 7 (notebooks)

James has notebooks is :

                7 + 4 = 11 (notebooks)

                      Answer : 11 notebooks

Mai has notebooks number is :

                3 + 4 = 7 (notebooks)

James has notebooks is :

                7 + 4 = 11 (notebooks)

                      Answer : 11 notebooks

Mai có số máy tính xách tay là:

                3 + 4 = 7 (máy tính xách tay)

James có máy tính xách tay là:

                7 + 4 = 11 (máy tính xách tay)

                      Trả lời: 11 máy tính xách tay

May I add "further than Pythagoras" to the last row ?

Columbus ran : (40 + 70) x 2 = 220 (feet)

Pythagoras ran : \(2\sqrt{40^2+70^2}=20\sqrt{65}\left(feet\right)< 20\sqrt{121}=220\)

So,Columbus ran : \(220-20\sqrt{65}\approx58,755\) (feet)

Let ABCD, M, N be the name of the triangle, the midpoint of AB and AD respectively. We have :

\(S_{AMN}=\dfrac{AM.AN}{2}=\dfrac{\dfrac{AB}{2}.\dfrac{AD}{2}}{2}=\dfrac{S_{ABCD}}{8}=\dfrac{1}{8}\)