COMIC : SCIENCE: MATHS CHALLENGES

The time has come for the maths challenges.Students are invited to solve different problems uploaded by maths teachers from all partner schools.I hope to cooperate with the maths teachers too.The problem will be uploaded every two weeks and students must send the solutions to Lithuania in ten days maximum. We will publish the best solutions, pictures and we will inform everybody who was the first to solve the problem.

Let`s start and good luck.

Challenge 1
There are two ducks ahead of the other two ducks.
There are two ducks behind other two ducks.
There are two ducks next to the other two ducks.
How many ducks are there?

Solution

There are 4 ducks.

Challenge 2

You have a cannon and two identical cannon balls. You take the cannon to a large open location that is perfectly flat and you adjust the cannon barrel so that it is perfectly level.

You load one of the cannon balls into the cannon and you hold the other cannon ball at the same height as the barrel. You fire the cannon and drop the other cannon ball at the same time.

Which cannon ball will hit the ground first?

Solution:

Both cannon balls should hit the ground at the same time, since gravity acts equally on two objects having the same mass. The cannon barrel was leveled and the cannon ball would begin to fall as it moved forward out of the barrel at the same rate as the cannon ball that was dropped by hand. They would hit at the same time but the cannon ball fired from the cannon would hit the ground far away.

Challenge 3 (for 14-15 years old students)
The same letters mean the same numbers. Find the meanings of the letters with which this equality is right.

Solution:a-5; b-2; c-4; e-7; d-1;f-6; g-3

Challenge 4 (for 13-14 years students)

Find the numbers

Can you find two numbers composed only of ones which give the same result when you add them and when you multiply them? Of course 1 and 11 are very near, but these are not the numbers which you must find, because if you add them you will have 12, and if you multiply them you will have only 11.

Solution: The two numbers are 11 and 1,1.

Thanks Spanish students for the right answer.

Challenge 5 (for 14-15 years students)

If 2 + 3 = 10

7 + 2 = 63

6 + 5 = 66

8 + 4 = 96

How many will be 9+7=?

Solution: 2 x (2+3) = 10

7 x (7 + 2) = 63

6 x ( 6 + 5) = 66

8 x (8 + 4) = 96

9 x (9+7)= 144

Congratulation Spanish students

Challenge 6 (for 13-14 years students)

1x1≠ 40

Add the same number to each number and make this inequality equal.

Solution:
13x31=403

Challenge 7 ( for 10-11 years students)

You have two jugs, one of them holds 3 litres of water and the other holds 5 litres.
How can you get exactly 7 litres in two jugs?

Solution:
Fill the 5-litre jug.
Pour three litres from this jug into the 3-litre jug, then pour the three litres away. So there is still two litres in the 5-litre jug.
Now pour these two litres into the 3-litre jug and fill the 5-litre jug.
You now have 7 litres.

Challenge 8 (for 13-14 years students)

a	b	c
d	e	f
g	h	i

a ∙ b ∙ c = 1 a ∙ d ∙ g = 1

d ∙ e ∙ f = 1 b ∙ e ∙ h = 1

g ∙ h ∙ i = 1 c ∙ f ∙ i = 1

a ∙ b ∙ d ∙ e = 2

b ∙ c ∙ e ∙ f = 2 e = ???

d ∙ e ∙ g ∙ h = 2

e ∙ f ∙ h ∙ i = 2

Solution:

e= 16

2	1/4	2
1/4	16	1/4
2	1/4	2

Challenge 12 (for 10-11 years students)

A piece of string measures 2/3 m. Without the use of any other measuring tools, how would you use the string to measure 1/2 m?

Answer for challenge 12

We bend the string in two equal halves. This is equal to 1/3 of the meter. We bend it again in two equal halves. This is 1/6 of the meter. We cut it off and the rest of the string is half a meter.

Pupils of Gymnasio Soufli.

Answer for challenge 12 from Poland

Solution by Lithuanian students

Begin by folding the string in half along its length; this will be 1/3 m.

Fold the 1/3 m length in half, giving 1/6 m.

Finally fold the 1/6 m length back along the length of the string.

The remaining length will be 2/3 1/6 = 1/2 m.

Challenge 14

Cut the Cross Puzzle

With two straight lines, cut the Swiss Cross into four congruent pieces which then fit together to make a square.

Solution

Challenge 15

Birds in Trees

There are 2 trees in a garden (tree "A" and "B") and on the both trees are some birds.

The birds of tree A say to the birds of tree B that if one of you comes to our tree, then our population will be the double of yours.

Then the birds of tree B tell to the birds of tree A that if one of you comes here, then our population will be equal to that of yours.

Now answer: How many birds in each tree?

Challenge 16

A set of weighing scales measures weight in kilograms. A boy, a girl, and a dog stand on the scales in three different ways.

How heavy would the boy, girl, and dog weigh together?

Solutions by Greek students