PUZZLE 12: 22nd-28th March (to be e-mailed by the 29th March)
POSTED BY IES CAMPANAR
A BALL GAME
A box holds 40 juggling balls. Two friends are playing a game in which they alternate to pick up balls from the box. When it is their turn each player can take out as many balls as wanted but never more than half the number of balls in the box. The player that cannot take any more balls from the box will lose. Who will be the winner, the first or the second friend to play? And which will be the right strategy to win the game?
SOLUTION
Let us see if there is a winning strategy. If there is one, the winner in his/ her last turn, should leave the other person only one ball as that would make it impossible for the other player to pick up any balls.
And so, going backwards, the winner in the previous movement, should have left the other player with 3 balls. This way the “loser” could only have picked up 1 ball and leave the other 2. (W(n-1) = 2·1 + 1 = 3).
In the same way, in the last-but-one movement, the winner should have left W(n-2) = 2·3 + 1 =7,and in previous turns he/she should have left: W(n-3) = 2·7 +1 = 15, W(n-4) = 2·15 +1 = 31.
However, only the person playing FIRST can get to do that by picking up 9 balls on his/her first movement and leaving in the following 15, 7, 3 y 1 balls.
The winner thus will be the first person to play and to use the strategy explained above.
Monday 22 March 2010
Wednesday 17 March 2010
Monday 8 March 2010
FORTNIGHT'S PUZZLE 11
PUZZLE 11: 8th-14th March (to be e-mailed by the 15th March)
POSTED BY IES CAMPANAR
NAMES
Three people whose surnames are White, Red and Black happen to meet at a party. Shortly after introducing themselves, the lady says:
-‘It’s funny that our surnames are White, Red and Black and that there are here three people whose hair colours are exactly those three colours’.
The red-haired person answers:
-‘Yes, it really is but you have probably noticed that none of us has the colour corresponding to our surnames’.
-‘True!’ says the person called White.
If the lady hasn’t got black hair, who has it red?
SOLUTION
Mr/Ms White hasn’t got red haired because he/she speaks after the one who is red-haired. He/She hasn’t got white hair because this is his family name so he/she has black hair.
Mr/Ms Red has neither red nor black hair so this is the white-haired person.
The only possibility is for the person called Black to be red-haired. Apart from that the lady can neither be called White nor Black, who answers to her. Thus she is called Red.
SOLUTION: The person who has red hair is Mr. Black.
POSTED BY IES CAMPANAR
NAMES
Three people whose surnames are White, Red and Black happen to meet at a party. Shortly after introducing themselves, the lady says:
-‘It’s funny that our surnames are White, Red and Black and that there are here three people whose hair colours are exactly those three colours’.
The red-haired person answers:
-‘Yes, it really is but you have probably noticed that none of us has the colour corresponding to our surnames’.
-‘True!’ says the person called White.
If the lady hasn’t got black hair, who has it red?
SOLUTION
Mr/Ms White hasn’t got red haired because he/she speaks after the one who is red-haired. He/She hasn’t got white hair because this is his family name so he/she has black hair.
Mr/Ms Red has neither red nor black hair so this is the white-haired person.
The only possibility is for the person called Black to be red-haired. Apart from that the lady can neither be called White nor Black, who answers to her. Thus she is called Red.
SOLUTION: The person who has red hair is Mr. Black.
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