1. The Beaver Cup

The beaver called Bob is in charge of organising the annual Beaver Cup.  One hundred and twenty eight teams have entered, and the tournament will be played on a knockout basis, so that once a team is beaten they are eliminated from the competition.

Bob is in charge of booking football pitches for the tournament, and he needs to know how many matches there will be in total. Can you help him?

If an extra 40 enter the tournament, bringing the number of teams to 168, how many matches in total would be played?

2. Climbing the Freedom Tower

The Beaver called Bob is trying to work out how long it will take him to climb the Freedom Tower. The tower is 300 metres high, and Bob climbs 6 metres per minute but slips back 3 metres per minute. How many minutes will it take him to reach the top of the Freedom Tower?

 3. Ball in pipe

Some squirrel youngsters have left their tennis fall to the bottom of a long, narrow vertical pipe which is cemented into the ground. They can see the ball through the hole on the top of the pipe, but cannot reach it.  They have nothing long enough to reach the ball, and they cannot dig a hole underneath the pipe.

Can you help the squirrels to get their tennis ball out of the pipe?

 4. All frogs are liars

The spiders are looking for someone to work in the wood wide web. They want somebody who will be honest and trustworthy. A number of frogs have applied, but the spiders then meet a frog who tells them that ‘All frogs are liars.’ Can this statement be true?

5.  Squirrels’ homework

The squirrel youngsters’ teacher has given them a problem to solve. If they get it right, they will get homework off tomorrow. Can you help them to solve the problem?

 Four 4 men below are all wearing a either a black or a white hat. They are standing in rising water:

• They cannot move and can only look forward
• There is a brick wall between A and B which they cannot see through
• They know that between them are 4 hats, of which 2 are black and 2 are white, but none of the men knows which colour he is wearing
• In order to stop the level of the water rising and drowning, one of them must call out the correct colour of the hat that he is wearing
• They are not allowed to move or talk to each other and have 10 minutes to figure it out

Which of the men calls out and how does he work out which colour hat he is wearing?

6. Creamy problem

Two frogs have fallen into a large bowl of cream. One believes everything that the brown bear says, and she is therefore very pessimistic about her chances of getting out. Consequently she decides not to try very hard to escape, and she sinks to the bottom of the bowl and drowns.

The other frog believes everything that the farm bull says, and she is optimistic that she can escape from the bowl. Can you help her to get out?

7. Poker school

Late one evening, the goat police arrive at Bob’s school for flying birds. A large sum of money has been stolen from the Riverbank, by a beaver whose name is Frank. The goat police don’t know what he looks like, but they are aware that he is gambling the money he has stolen at the poker school.

There are four beavers playing at the poker school. One works with the Beaver Construction Company, the second is a teacher, the third is employed at the wood wide web, and the fourth works in the nearby hospital. The goat police immediately arrest the beaver who works with the Beaver Construction Company.

How did they know that this beaver was the thief? 

8. Catching the train 

The rat is on his way to a bankers’ conference, and he is trying to catch a train. He is able to run at 12 kilometres per hour, and the train which is 100 metres away, is moving at 45 kilometres per hour. The rat catches the train and arrives on time for the bankers’ conference. How does he manage to do it?  

9. Murder trial

A hawk was on trial for murdering Cock Robin, and everyone believed that he was guilty. The hawk’s legal fox surprised the court by saying that in thirty seconds Cock Robin would enter the courtroom through the back door.

The animals on the jury stared at the courtroom door, but of course Cock Robin failed to appear as he was already dead. The hawk’s legal fox argued that the jury would not have stared at the courtroom door unless they believed that Cock Robin could still be alive, and that therefore that the hawk could be innocent.

Later, the same day, the hawk was convicted of murdering Cock Robin. What made the jury so certain that he was guilty?

10. Cat race

Two cats were having a swimming race across the river at the River Bank. One cat was called ‘One-two-three’, and the second cat was called ‘Un-deux-trois’.

Which cat won the swimming race? 

1. The Beaver Cup
   
   Bob will have to book pitches for 127 matches if there are 128 teams. If there are 168 teams there will be 167 matches.
   
   Basically, in a knockout competition, only one team does not lose (i.e. the eventual winner of the competition), and a team can only lose once. Thus, the number of matches to be played is always one less than the number of teams.
   
    
2. Climbing the Freedom Tower
   
   It will take Bob 99 minutes to reach the top of the Tower.
   
   After 98 minutes he will have climbed up 294 metres (i.e. (98 x 6) – ( 98 x 3)). On the 99th minute he will climb 6 metres and he will therefore have reached the top of the Freedom Tower.
   
   
   
3. Ball in pipe
   
   The squirrel youngsters can get the ball out by filling the pipe with water. The ball will then float to the top of the pipe.
   
    
4. All frogs are liars
   
   This statement cannot be true. All frogs must include the frog who makes the statement ‘All frogs are liars’.  If he is a liar, and he must be for the statement to be true, then the statement must be false. Therefore, all frogs cannot be liars.   
   
    
5. Squirrels’ homework
   
    A cannot answer as he cannot see beyond the wall and therefore he cannot tell what hat anyone, including himself, is wearing.
   
   B is in a similar position.
   
   D cannot answer because he can see only B and C who are wearing a white and black hat respectively. He knows that A can also have a black or white hat, and therefore so can he. 
   
   C knows that B is wearing a white hat. If C was also wearing a white hat, C knows that D would see two white hats in front of him. D would then know that both A and D were wearing black hats, and he would be able to call out to this effect.
   
   As D stays silent, C realises that C must have a black hat himself.
   
    
6. Creamy problem
   
   The optimist frog didn’t give up, having fallen into the bowl of cream. She continued to swim around as fast as she could, until eventually she was sitting on top of a large mound of butter
   
    
7. Poker school
   
   The beaver who works with the Beaver Construction Company was the only male beaver, and therefore he was the only one whose name could have been Frank.
   
    
8. Catching the train
   
   The train is moving towards the rat, not away from him.
   
    
9. Murder trial
   
   The hawk was the only animal in court who did not stare at the courtroom door, waiting for Cock Robin to appear.   
   
    
10. Cat Race
    
    The ‘One-two-three’ cat won the race because the ‘Un-deux-trois’ cat sank;  (The French number five is cinq – pronounced sank).