The road piece has to join the cat to the milk and the mouse to the cheese, yet keep those two routes from ever touching.
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Hint 2 of 2
Look at which sides of the missing square each road must enter and leave, then find the piece whose roads connect exactly those sides without crossing.
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Approach: match the road piece to the required connections
The cat must reach the milk, and the mouse the cheese, but the two animals' paths must stay separate.
So the missing piece needs two roads that link the correct opposite sides while never meeting in the middle.
Only the curved piece E carries the two routes past each other without letting them join.
In a cafe the soup costs €4, the main course €9 and the dessert €5. The three courses ordered together cost €15. How many euros cheaper is this than ordering the same three courses separately?
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Answer: A — €3
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Hint 1 of 2
First add up the three separate prices.
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Hint 2 of 2
Then compare that total with the combined price of 15.
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Approach: compare separate total with bundle price
Four friends each eat some ice cream. Mike eats more than Franz, Jaroslav eats more than Veit, and Jaroslav eats less than Franz. Put the friends in order by how much ice cream they ate, starting with the largest amount.
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Answer: C — Mike, Franz, Jaroslav, Veit
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Hint 1 of 2
Turn each clue into a simple "more than" comparison and chain them together.
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Hint 2 of 2
Jaroslav eats less than Franz but more than Veit, and Mike eats more than Franz.
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Approach: chain the inequalities into one order
Mike > Franz, Jaroslav > Veit, and Jaroslav < Franz.
Combine: Mike is biggest, then Franz, then Jaroslav, then Veit.
Largest first: Mike, Franz, Jaroslav, Veit — option C.
Eva is a centipede with exactly 100 feet. Yesterday she bought 16 pairs of shoes and put them on right away. Even so, she still had 14 feet with no shoes. On how many feet was she already wearing shoes before she went shopping yesterday?
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Answer: C — 54
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Hint 1 of 2
Each pair of shoes covers 2 feet; first find how many feet have shoes now.
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Hint 2 of 2
Subtract the feet she put new shoes on today from the total now wearing shoes.
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Approach: count shod feet, then remove today's new shoes
She has 100 feet and 14 are bare, so 100 − 14 = 86 feet wear shoes now.
Today she put on 16 pairs = 32 shoes, covering 32 feet.
So before shopping she already wore shoes on 86 − 32 = 54 feet.
Matthias and Klara live in a tower block. Klara lives 12 floors above Matthias. One day Matthias climbs the stairs to visit Klara. When he is halfway there he is on the 8th floor. On which floor does Klara live?
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Answer: B — 14th
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Hint 1 of 2
Halfway up the climb, Matthias has gone up half of the 12 floors.
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Hint 2 of 2
Find Matthias's floor first, then add 12 for Klara.
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Approach: use the halfway floor to find the start
Half of the 12-floor climb is 6 floors, and that point is the 8th floor.
A large cube is made from 64 small cubes. The 5 visible faces of the large cube are green and the bottom face is red. How many of the small cubes have 3 green faces?
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Answer: A — 4
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Hint 1 of 2
A small cube shows 3 green faces only if it is a corner of the big cube with all three faces on green sides.
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Hint 2 of 2
The bottom face is red, so bottom corners can't have 3 green faces — only the top corners can.
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Approach: check which corner cubes touch three green faces
Only corner cubes can show three faces.
The four bottom corners each touch the red bottom, so they have at most 2 green faces.
The four top corners each touch the green top and two green sides — 3 green faces.
A ferry boat can carry, in one trip, either 10 cars or 6 lorries. Yesterday the boat crossed the river 5 times. It was always full and carried 42 vehicles in all. How many of these were cars?
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Answer: E — 30
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Hint 1 of 2
Each of the 5 full trips carries either 10 cars or 6 lorries.
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Hint 2 of 2
Start by pretending every trip was lorries, then see how far short of 42 you are.
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Approach: start from all-lorry trips and swap until the total is right
If all 5 trips were lorry trips, that would be 6 + 6 + 6 + 6 + 6 = 30 vehicles, which is 12 short of 42.
Changing one lorry trip (6) into a car trip (10) adds 4 vehicles, and 12 needs three such changes.
So 3 trips were car trips: 10 + 10 + 10 = 30 cars, choice E.
Hans started a chain e-mail. He sent an e-mail to his friend Peter, who sent it on to 2 more people. Each person who gets the e-mail sends it on to 2 more people. After 3 rounds, 1 + 2 + 4 = 7 people have received the e-mail. How many people have received the e-mail after 5 rounds?
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Answer: C — 31
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Hint 1 of 2
Each round doubles the number of new people: 1, 2, 4, then 8, 16.
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Hint 2 of 2
Add up the new people from all five rounds.
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Approach: sum the doubling rounds
Each round the number of new people doubles: 1, 2, 4, then 8, then 16.
On the playground some children measure the length of the playground in strides. Anni takes 15 strides, Betty 17, Denis 12 and Ivo 14. Who has the longest stride?
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Answer: C — Denis
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Hint 1 of 2
They all cross the same length, so fewer strides means each stride is longer.
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Hint 2 of 2
Find who used the fewest strides.
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Approach: fewest strides means the longest stride
The playground length is fixed, so the longest stride belongs to whoever takes the fewest steps.
The teacher said, “In our school library there are roughly 2010 books.” The pupils then guessed exactly how many there are. Artur guessed 2010, Beate guessed 1998 and Carlos guessed 2015. Their guesses are off by 12, 7 and 5, but not in that order. How many books are in the library?
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Answer: A — 2003
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Hint 1 of 2
The real number differs from the three guesses by 12, 7 and 5 in some order.
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Hint 2 of 2
Try a value near 2010 and check that its distances to 2010, 1998 and 2015 are exactly 12, 7 and 5.
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Approach: find the value whose distances to the guesses are 12, 7, 5
Lines are drawn on a piece of paper and some of the lines are numbered. The paper is cut along some of these lines and then folded as shown in the picture. What is the total of the numbers on the lines that were cut?
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Answer: D — 20
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Hint 1 of 2
A line is cut only if the fold could not bring its two sides together; uncut lines are the fold creases.
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Hint 2 of 2
Figure out which numbered lines stayed as folds, and add up the rest.
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Approach: separate fold creases from cut lines, then add the cut numbers
Match the folded result to the flat sheet to see which lines were creases and which were cut.
Andrew, Stefan, Robert and Marko meet at a concert in Zagreb. They come from different cities — Paris, Dubrovnik, Rome and Berlin (not necessarily in this order).
• Andrew and the friend from Berlin arrive first in Zagreb. Neither of these two has ever been to Paris or Rome. • Robert is not from Berlin, but he arrives together with the friend from Paris. • Marko and the friend from Paris enjoyed the concert very much.
Which city does Marko come from?
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Answer: D — Berlin
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Hint 1 of 2
Andrew is not from Paris, Rome, or Berlin, so his city is forced.
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Hint 2 of 2
Place each person's city one clue at a time until only Marko's is left.
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Approach: eliminate cities person by person
Andrew and the Berlin friend are two people, and Andrew hasn't been to Paris or Rome, so Andrew is from Dubrovnik.
Robert isn't from Berlin and arrives with the Paris friend, so Robert is from Rome.
That leaves Paris and Berlin for Stefan and Marko; since Marko isn't the Paris friend, Marko is from Berlin.
Berti’s friends each add together the day and the month of their birthday. They all get the answer 35, but no two of them have the same birthday. What is the largest number of friends Berti can have?
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Answer: B — 8
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Hint 1 of 2
You need months and days with month + day = 35, and each birthday must be a real date.
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Hint 2 of 2
Start from December and step down through the months, checking the day fits that month.
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Approach: count valid (month, day) pairs summing to 35
List month + day = 35 with a valid day: Dec 23, Nov 24, Oct 25, Sep 26, Aug 27, Jul 28, Jun 29, May 30.
April would need day 31, which doesn't exist, and earlier months need impossible days.
That gives 8 different birthdays, so at most 8 friends.
