Question

1. Rabbits are sawing a log. They made 10 cuts. How many blocks of wood did they get? (the answer is a number)

2. Friends are cutting a donut into sectors. They made 10 cuts. How many pieces of a donat did they get? (the answer is a number)

3. Rabbits are sawing several logs. They made 10 cuts and got 16 blocks of wood. How many logs did they saw in the beginning? (the answer is a number)


4.In the bag, there are balls of two colors: black and white. What is the minimum number of balls one should take out from the bag (not looking) to be sure to get balls of different colors? (the answer is a number)

5.John's cat always sneezes before the rain. The cat sneezed today. "It means it is going to rain" - thinks John. Is John right?

6.How many squares formed by sticks do you see in the picture? (the answer is a number)
Captionless Image

Answer 1

1)

While sawing a log, if n cuts are made, number of pieces = n+1

Therefore when 10 cuts are made, made, number of blocks of wood = 10+1 = 11

2)

While cutting a donut into sectors, if n cuts are made, number of pieces of donut = n

Therefore when 10 cuts are made, made, number of pieces of donut = 10

3)

Let us assume that the number of logs sawed in the beginning = x

If n cuts are made in a log, number of blocks of wood in that log = n+1

Let ni represent the number of cuts in log i

n1+n2+ ... nx = 10

Also

(n1+1)+(n2+1)+ .... (nx+1) = 16

(n1+n2+...nx) +x = 16

10+ x = 16

x=6

Therefore number of logs sawed in the beginning is 6

4)

If there are n black balls and m white balls

Case 1

n>m

Then

we have to take n+1 balls

Case 2

m>n

Then

we have to take m+1 balls