Question

I need answers as soon as possible

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?

Answer 1

1)

For n cuts, we get n+1 pieces

So they get 11 blocks of wood for 10 cuts.

2)

For n cuts in a donut in the form of sectors we get n pieces.

So for 10 cuts of donut they get 10 pieces in the form of sectors.

3)

Let the logs be n

for n=1 and 10 cuts we get 11 pieces

for n=2 and 10 cuts(sum of cuts in all logs = 10) we get 12 pieces

for n=3 and 10 cuts(sum of cuts in all logs = 10) we get 13 pieces

Therefore we can generalise,

no of pieces = no of cuts + no of logs

16 = 10+n

n = 6 logs

4)

Let us assume there are n balls in total of which x are white and y are black. (x+y=n)

If x>y, then

min number of balls one should take out from the bag (not looking) to be sure to get balls of different colors = x+1

If y>x, the

min number of balls one should take out from the bag (not looking) to be sure to get balls of different colors = y+1

If x=y=n/2

min number of balls one should take out from the bag (not looking)to be sure to get balls of different colors = (n/2)+1

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?

The above statement doesnt mean whenever cat sneezes it will rain.

So John is wrong.