a) There are :7 x 7 x 6 x 5 = 1470 numbers

b) There are :4 x 4 x 3 x 2 = 96 even numbers

There are : (200 - 1) : 1 + 1 = 200 numbers from 1 to 200

We have a sequence of two-digit numbers are as follows :

2 ; 12 ; 22 ; 32 ; ....... ; 192

Apply a formula to count numbers , we have :

(192 - 2) : 10 + 1 = 20 

There are also numbers with 2 digits such as

20 ; 21 ; 23 ; 24 ; .... ; 29 ; 120 ; 121 ; 122 ; 123 ; ...... 129

And there are have 18 also numbers .

So , from these information , we have 38 numbers have digit 2

We have :

200 - 38 = 162 (numbers)

There are 162 numbers from 1 to 200 do not have the digit 2 

Land : A = 1.3 + 3.5 + 5.7 + ...... + 99.101

=> 4A = 1.3.(5 - 1) + 3.5.(7 - 3) + ...... + 99.101.(103 - 99)

=> 4A = 1.3.5 - 1.3.5 + 3.5.7 - 3.5.7 + ...... + 99.100.101

=> 4A = 99.100.101

=> A = 99.100.101/4

=> A = 249975

There are 4 right angles of a square.

Numbers sweet is the biggest that he can get from the shop is : 

                                         30 : 3 = 10 (sweet)

                                                 Answer : 10 sweet 

The edge length of the cube is :

3√2162163 = 6 (cm) because 6 x 6 x 6 = 216 

The area is :

6 x 6 = 36 (cm2)

Change : half an hour = 0,5 hour

The speed of the car is :

   ( 25 - 5 ) : 0,5 = 40 ( km / hour )

Answer : 40 km / hour

The distance between the houses is: 3000: 100 = 30 (minute)
Homeownership is: 3000: 150 = 20 (minutes)
Average by John in a minute: 3000: (20 + 30) = 60 (minute)

Answers:60 minute

Let A be the least number we have to find.

So A - 5 is the LCM(15; 18; 9; 12) = - 180

Then A = - 175

We have : 37 = 3 + 5 + 29 (c1)

                 37 = 3 + 11 + 23 (c2)

                 37 = 5 + 13 + 19 (c3)

Drees is three ways are there to write 37 

You have : 300 = 22.3.52

The number of integer factors 300 have is :

                      2.[(2 + 1)(1 + 1)(2 + 1)] = 36

                               Answer : 36. good

( a = odd number ) 

 a.(a+2)= ( a+1)^2-1

Good ^^

123476543 = 11111 x 11113

Let n be the smallest value of that number. When n is divided by 2,3,4,5,6,the remainder is always 1,so n - 1 is divisible by 2,3,4,5,6

=> n - 1 = LCM(2,3,4,5,6) = 60 => n = 61

We have : 3 - 2 = 4 - 3 = 5 - 4 = 6 - 5 = 1

So n + 1 is divisible by 3,4,5,6 but we need to find the smallest value of n.

=> n + 1 = LCM(3,4,5,6) = 60 => n = 59

1339 = 103 x 13 = 1 x 1339.

No one can be 1339 years old, so the grandfather will be 103 years old and his grandchild will be 13 years old next year.

Thus, the grandfather is 102 years old, and his grandchild is 12 years old now.

We have : ƯCLN(140;240) = 20

Dress the largest square can be 20 cm x 20 cm

Put A = 1.3 + 3.5 + 5.7 + ...... + 99.101

=> 4A = 1.3.(5 - 1) + 3.5.(7 - 3) + ...... + 99.101.(103 - 99)

=> 4A = 1.3.5 - 1.3.5 + 3.5.7 - 3.5.7 + ...... + 99.100.101

=> 4A = 99.100.101

=> A = 99.100.101/4

=> A = 249975

The NUMBER of pairs (m;n) ... 

Have: n3 - 3n2 + 2 = n3 - n2 - 2n2 + 2

= n2(n - 1) - 2n2 + 2

It is easy to see that n2(n - 1) is an even number because it contains n(n - 1) which is the product of two consecutive natural numbers, so n2(n - 1) - 2n2 + 2 is an even number

But n3 - 3n2 + 2 = n2(n - 1) - 2n2 + 2 is a prime number so n3 - 3n2 + 2 = 2

=> n3 - 3n2 = 0 

<=> n2(n - 3) = 0

According to the topic, n should be positive n =