Grade 5 Mathematics Olympiad exercises with answers .

The speed of the water is 4 kilometers per hour. Now it takes 5 hours for a boat to sail 60 kilometers of river against the water, and how many hours does it take to sail downstream?

1 There are 100 chickens and rabbits, and the number of legs of chickens is 28 less than that of rabbits.

Solution: 4*100 400,400-0 400 Suppose they are all rabbits, there are a total of 400 rabbits' feet, then the chicken's feet are 0, and the chicken's feet are 400 fewer than the rabbit's feet.

2 A cloth bag contains gloves of the same size but different colors, black, red, blue, yellow four colors, ask at least how many gloves to ensure that there are 3 pairs of the same color?

Solution: You can look at four different colors as 4 drawers, and gloves as elements, to ensure that there is a pair of the same color, that is, there are at least 2 gloves in 1 drawer, and according to the drawer principle, at least 5 gloves must be touched. At this time, take out a pair of gloves of the same color and have 3 gloves left in the back 4 drawers.

According to the drawer principle, as long as you find 2 more gloves, you can ensure that there is a pair of gloves of the same color, and so on.

Think of the four colors as 4 drawers, to ensure that there are 3 pairs of the same color, first consider ensuring that there is 1 pair of gloves to find 5 gloves. At this time, after taking out one pair of the same color, there are still 3 gloves left in the 4 drawers. According to the drawer principle, as long as you find 2 more gloves, you can ensure that 1 pair is the same color.

And so on, to ensure that there are 3 pairs of gloves of the same color, a total of 5 + 2 + 2 = 9 (only).

A: You need to find at least 9 gloves to ensure that there are 3 pairs of the same color.

3 There are a number of blocks of four colors, each person can take 1-2 pieces, at least how many people can take it, in order to ensure that 3 people can get exactly the same? The answer is 21

Solution: There are 4 different ways to take 1 piece per person, and 6 different ways to take 2 pieces per person.

When there are 11 people, it is guaranteed that at least 2 people will achieve exactly the same:

When there are 21 people, it is guaranteed that there are only 3 people who achieve exactly the same.

23 kg is tung oil!

Because cottonseed oil weighs twice as much as rapeseed oil, the sum of the weights of these two oils is divisible by 3. The total weight of 6 barrels of oil is 107kg, so the weight of 1 barrel of tung oil should be divided by 3 by 2, so 23kg is tung oil!

2 (80 20) = 8 (root).

The least common multiple of 4 and 5 is 20, so that the dyeing will have a cycle change, and the equation is: 80 (4 5) = 4 cycles.

There are 2 1 cm sticks in each cycle (you can think of the left-to-right stained as the right-to-left stained).

3.A football match was held in the seventh grade of a middle school, stipulating: 3 points for a win, 1 point for a draw, 0 points for a loss, and a total of 8 points for a seven-year class 1 game, of which the number of wins and draws is the same, and the loss is 1 more than the win, how many wins, draws, and losses?

Solution: Set the number of games to be won as x

3x+1x+0*(x+1)=8

4x=8x=2 wins, 2 wins.

Draw 2 and lose 3.

The water in bucket A is two-thirds of bucket B, and if you pour half of the water in bucket B into bucket A, what fraction of the water in bucket A is in bucket B?

In the end, each monkey has 9 peaches in their hands.

Reverse thinking. Monkey C snatches half from Monkey A and eats one. Then there are 9 of them each.

Before eating 1, C is 10.

What about before you grab half of it? A should have 18, while C should have 1.

Monkey B snatches half from monkey C and eats one.

Before eating one, B should be 10.

Before half of the grabbing, B was still 9, and C should be 2.

Monkey A snatches half of it from Monkey B and eats one.

At this point, A has 18, and before eating 1, A has 19.

Before half of the grabbing, A should have 10 and B 18.

In summary, there are 10 in A, 18 in B, and 2 in C.

The three monkeys, A, B, and C, each have a number of peaches. Monkey A snatches half (A19B9) from Monkey B (A19B9) and eats one (A18B9). Monkey B snatches half (B10C1) from Monkey C (B9C2) and eats one (B9C1).

The monkey snatches half (C10A9) from monkey A (C1A18) and eats one (C9A9). In the end, each monkey has 9 peaches in their hands. How many peaches did they have?

Let A be x, B be y, and C be z, then: after A grabs B, A has: (x+y 2)-1

B has: y 2

After B grabs A, A has: (x+y 2-1) 2

B has: y 2+(x+y 2-1) 2-1

After A grabs C, A has: (x+y 2-1) 2+z 2-1 C has: z 2

From the question: z 2 = 5

x+y/2-1)/2+z/2-1=11

y/2+(x+y/2-1)/2-1=11

Solution: x=y=z=10 (pcs).

That is, each monkey has 10 peaches.

Happy o(o

After C robbed half of A, there were 9 left, so it means that the other half of A was also 9 at this time, so C was 1 before Grabbing A. A is 18, and after grabbing B, A is 19.

B robbed half of C, so C started with 2. I was robbed of 1 by B.

Before B robbed C 1, it was 9+1-1=9, so it can be seen that B was robbed by A 9. So A starts with 19-9=10 and B has 10*2=18.

A = 10, B = 18, C = 2

It's pretty much the same as the one above.

There are a total of 3*9+3 30 peaches.

Monkey C snatches half from Monkey A and eats one. Then there are 9 of them each.

Before eating 1, C is 10.

What about before you grab half of it? A should have 18, while C should have 1.

Monkey B snatches half from monkey C and eats one.

Before eating one, B should be 10.

Before half of the grabbing, B was still 9, and C should be 2.

Monkey A snatches half of it from Monkey B and eats one.

At this point, A has 18, and before eating 1, A has 19.

Before half of the grabbing, A should have 10 and B 18.

In summary, there are 10 in A, 18 in B, and 2 in C.

If the sum of a four-digit number and a three-digit number is 1999, and the four-digit number and three-digit number are made up of 7 different numbers. So, how many such four-digit numbers can there be at most?

This is the fourth question of the third major question in the final paper of the 15th "Spring Festival Cup" Mathematics Competition for primary school students in Beijing, and it is also the question that the contestants have lost the most points.

A 1, B e 9, (E≠0), C f 9, D g 9 are obtained.

In order to calculate the maximum number of such four-digit numbers, the conditions a, b, c, d, e, f, and g are different from each other, it can be seen that there are 7 choices for the number b (b≠1,8,9), 6 choices for c (c≠1,8,b,e), and 4 choices for d (d≠1,8,b,e,c,f). Thus, according to the principle of multiplication, such a four-digit number can have a maximum of (7 6 4=) 168.

Solution: Let these two numbers be x,y(x y) respectively

When these two numbers are coprime (1).

x-y=30

xy-1=450

x squared - 30x - 451 = 0

x-41][x+11]=0

x = 41 or x = -11

x cannot be negative.

x=41,y=11

When y is the divisor of x (2).

x-y=30

x-y=450

Apparently (2) is not valid.

x=41,y=

A:

Let's say the rabbit distance is.

Then the time for the rabbit to go up and down the mountain is 6

So the rabbit's.

Average. is 2 (1 3 + 1 6) = 4 (km hours).