Math Olympic Games

MATH OLYMPIC GAMES

24/05

WELCOME!TervetuloaHoşgeldinizWitamybenvenutIBIENVENIDOS

Zespol Szkol w KorczynieSäynätsalon yhtenäiskouluICS Michelangelo BuonarrotiRukiye Koç OrtaokuluCompañia de Maria de Granada

According to the diagram on the left, there is a building with 5 floors. In this moment, an elevator is stopped in one of the floors. In each floor there is a worker awaiting for the elevator to arrive to the floor where she is working. The number depicted on the clothes of every worker indicates the floor where that worker wants to go. If the elevator can carry in thirteen steps to all the workers from their current position to their respective floors (one “step” equals one movement of the elevator from a floor to the immediate upper or lower one), the challenge consists on discovering in which floor the elevator is currently. The elevator has room for only one worker at a time.

The elevator is on floor number 2 (it takes 13 steps to put every worker in the floor where they want to go) :)

The 7-life catNone, a small but witty cat, fell through the window of a 100-floor building, but surprisingly, it survived. Could you explain how this is possible?

None the cat fell through the window of the first floor, so he didn't suffer any damage :)

A part of a squareWhich part of the square is shadowed in the following shape? Is it more or less than its half?

This image proves that it is exactly half of the square.

The mistery of the magic ticket sellerA man goes to the cinema and when he arrives to the ticketbox he sees a signpost explaining that each ticket costs 3€. He gives the ticket seller 10€ and he, immediately gives him 3 tickets. How did the ticket seller know that the man wanted to buy 3 tickets and not 2 or 1?

The man gives the ticket seller 10€ in coins of 2€, so it is obvious that he wants 3 tickets, because if he wanted 2 tickets, he would have given him less money.

FIGURES AND LETTERSTeacher Merja gave us the figures 5, 7, 20, 2, 2 and 72. We had to get to the target number: 44. How did we do it?

You can obtain the exact number by following these steps:20 x 2 = 40; 7 - 5 = 2; 40 + 2 = 42; 42 + 2 = 44

FlagsAfter some lessons devoted to memorizing flags and more flags, teacher Anna asked us if we knew what have in common the flags from Bangladesh, Great Britain, Israel, Japan, Laos, Micronesia, Nigeria, Switzerland, Thailand and Botsuana. No one could find the solution, can you?

All the flags are symetric. If we place them the other way round, nobody would notice ;)

An unbalanced scaleOur PE teacher, at the beginning of the year, fills in a paper with some of our data, for example, our weight. The problem is that the school’s scale is unbalanced, so it weights over or below, always the same number of kilos. It showed that Dorian's weight is 43kg, for John it was 48kg and when they weighed together, it showed 88kg. Using those data, could you figure out their real weights?

If we add up the weight shown by the scale when we weigh separatedly, it will show 43 + 48 = 91 kg. But when we do it together, the scale only shows 88 kg, so the scale weighs 3 kilos too many, so Dorian's real weight is 40 kg, while John's is 45 kg.

The three clocksOne of my family’s favourite hobbies is collecting watches, no matter if they work or not. I don’t know why they need so many if they all can see the time in their cellphone, but what is most shocking to me is why they want those not working. One of my favourite ones is one hour and a half behind the time, another one is 40 minutes ahead of time and another one that is just broken! I remeber once when I had the three of them together on the table, and they were showing the time you can see in the image. Could you guess the time that it was when I looked at them?

If the clock that is 40 minutes ahead is the one showing 10:00, the real time is 9:20. So, the one showing 11:00 would be 1hour and 30 minutes ahead, which is not a possible option.it is obvious that the one showing 8:50 cannot be the one ahead in time...Finally, the only option left is for the clock ahead in time to be the one showing 11:00, so it is actually 10:20, therefore, the one showing 8:50 is the one 1hour and 30 minutes behind and the one showing 10:00 is the one that does not work.

Breaking the squareCan you divide the following square in 8 different squares? The original size of the square is 4 x 4.

Roman numbersEvery year, our Math teacher explains to us how Roman numbers work. The first year was great because I had always felt curious about those letters that were numbers at the same time. The second year, I started to feel a bit bored. This year I haven’t paid attention at all. Well, I was thinking about them but something different: if we order them in alphabetical order, the first one is 100 (C), then 200 (CC), the third 300 (CCC) and one of the last ones would be 10 (X). Which one would be the last one if we order them alphabetically?

The last one would be number XXXVIII (38)

Rolling CharlieIt was Friday evening when me and my friends were really bored. We started thinking what would happen is we put a small LED light in the wheel of Charlie’s chair while one of us pushed it in a straight road. Each one of us believed that the light would follow a different direction (as you can see in the images). Which one of us was right?

Bruno is right

The golden ball

The Golden Ball is an award given to the best football player every year. Fill in the following chart with the clues offered and you will know the result of one of the past editions: Iniesta is 29 years old and he was not the first one. The third one is 1.7 metres high. Leo Messi is 26 years old and was one position behind Cristiano. The one who is 28 years old is 1.86 metres high. One of them is 1.69 metres high. Cristiano Ronaldo is not the last one.

Target achieved

Could you get 19 points accurate throwing 3 darts to the bullseye?

With four fives

Complete the following numeric equalities using only the four basic operations (+, -, x, /) and as many parenthesis as you may need:Note: Remember that each combined operation has got priority for parenthesis, next multiplications and divisions and finally, additions and substractions.

Sticks and Roman numbers

Could you move one stick from those in the image to make the equality true? And without moving any stick?

Sticks and Roman numbers solutions

The 6 pool balls

Could you move one stick from those in the image to make the equality true? And wPlace the 6 pool balls within the triangle so each ball is the result of substracting the two balls that are above it. To understand properly the problem, in image 1 there is a wrong example where numbers 2 and 1 are properly placed because 5-3=2 and 6-5=1, but number 4 cannot be below numbers 1 and 2, because 2-1= 1 and not 4.

Tangram

Form the arrow using the pieces on the right

Circles and dots

Draw the image that goes after these trhee:

My playground

If painting the wall on the figure marked with a) costs 40€, how much will it cost painting the square wall?

You can clearly see that the surface in b) is four times what measures the surface in A). Therefore, painting the big wall will cost us four times what costs painting the small one:4 x 40 = 160€

Getting the ball backOur table tennis ball has fallen into a vertical narrow pipe, 2m long, and closed on one side. How can we get it back out if we only have a table tennis racket, a piece of paper, a bottle of water, a rope, a pen and a tap with water flowing?

You can use the bottle and the tap to fill the pipe with water and the ball will little by little come up by its own.

Aliens from different planets

Join every pair of identical aliens with continous lines that do not go out of the rectangle or touch each other.

How many triangles can you count in the following image?

There are 8 small triangles, 4 medium-size triangles and other 4 big triangles. Total: 16 triangles

Can you divide the following moon in 6 parts using only two straight lines?

Alternating cup

Go from image 1 to image 2 moving only 1 cup

Take the second cup and pour the liquid into the fifth one ;)

Food is burningBartosz has got a problem. He must cook some food during exactly 11 minutes but he has got only two sandclocks, one of them lasts for 8 minutes and the other one, 5 minutes. How can he make it so food does not get burnt?

Bartosz must set both sandclocks at the same time. When the one of 5 minutes finishes, the one of 8 minutes has still got 3 minutes. Juan must turn the cooker on and wait for the 8 minute sandclock to finish. When it is empty, food will have been cooking for 3 minutes. Then, he only has to set the 8-minute sandclock and when it finishes, 11 minutes will have gone by.

With 10 newspapers we can make a new nespapr. How many newspaper can we get with 200 old newspaper? Note: In this case, a nesspaper can be recicled as much as we want.

With the initial 200 newspapers we can get 20 new newspapers, and when we recycle these 20 newspapers we can get another 2 newspapers, so in total we get 22 newspapers.

The 30 bottles

One father gives his sons 30 bottles. 10 bottles are completely full, 10 bottles are only half full and the other 10 bottles are fully empty. Each of the sons must get the same amount of liquid and the same amounf of bottles. How could you do it?

There are several solutions. Two examples:a) Son 1: 5 full bottles and 5 empty bottles. Son 2: 5 full bottles and 5 empty bottles. Son 3: 10 half-full bottles.b) Son 1: 3 full bottles, 4 half-full bottles and 3 empty bottles. Son 2: 3 full bottles, 4 half-full bottles and 3 empty bottles. Son 3: 4 full bottles, 2 half-full bottles and 4 empty bottles.

According to the image, what is the next element?

Which number must be write in 5 to follow the sequence?

In 1 appears 2 (1 x 2 = 2). In 2 appears 6 (2 x 3 = 6), in 3 appears 12 (3 x 4 = 12), in 4 appears 20( 4 x 5 = 20). So, in 5 must be 30( 5 x 6 = 30)

5 candles

If we have 5 lights lit and wind blows off 3, how many candles have we got left?

Even if wind blows off 3 candles, there are still 5 candles: 3 off and 2 lit.

How old am I?

Can you guess how old I am if I tell you that in 4 years I will be double the age that I was 5 years ago?

I am 14 years old. So, in 4 years I will be 18, which is double the age that I was 5 years ago: 9 years old.

How can we cut a cake in 8 identical parts using only 3 cuts?

You just have to make a horizontal cut in the middle of the cake and then, other two small perpendicular ones, so you divide each piece in four new pieces. This way you will have two floors with four pieces of cake in every floor.

THIS IS THE END, MY FRIENDS

Look ak the following sequence:ENDENDENDENDENDENDENDENDENDEND...If letter E goes in position number 1, which letter will be in position number 2000?

If letter E appears in position 1, 4, 7, 10...it means that they are one unit higher than the multiples of 3.Letter N appears in position 2, 5, 8, 11... so they are two units higher than the multiples of 3.Letter D appears in all the positions that are multiple of 3.So, 2000 = 666 x 3 + 2 and we know that number 2000 is two units higher than a multiple of 3. Therefore, in position 2000 we find an N.