Monday, 24 May 2010
FORTNIGHT'S PUZZLE 16
PUZZLE 16: 24th-30th May (to be e-mailed by the 31st May)
POSTED BY IES CAMPANAR
A NUMEROUS FAMILY
The product of my sons’ ages is 1664. The age of the eldest is the double of my youngest son’s age. I am 50 years old myself.How many sons have I got?How old are they?
SOLUTION
The factorial decomposition of 1664 is the product of 13 x 2 with exponent 7. Since 13 can be neither the youngest nor the eldest son, the solution is 2 with exponent 3 = 8, 13, and 2 with exponent 4 = 16. Therefore the three sons are: 8, 13 and 16 years old.
POSTED BY IES CAMPANAR
A NUMEROUS FAMILY
The product of my sons’ ages is 1664. The age of the eldest is the double of my youngest son’s age. I am 50 years old myself.How many sons have I got?How old are they?
SOLUTION
The factorial decomposition of 1664 is the product of 13 x 2 with exponent 7. Since 13 can be neither the youngest nor the eldest son, the solution is 2 with exponent 3 = 8, 13, and 2 with exponent 4 = 16. Therefore the three sons are: 8, 13 and 16 years old.
Monday, 10 May 2010
FORTNIGHT'S PUZZLE 15
PUZZLE 15: 10th-16th May (to be e-mailed by the 17th May)
POSTED BY IES CAMPANAR
AT THE CIRCUS
The most experienced trainer of a circus needs 40 minutes to wash an elephant, his son doing the same task in 2 hours. How long will it take them both to wash 4 elephants? How many elephants will each of them wash?
SOLUTION TO PUZZLE 2
In two hours the son washes one elephant while his father washes 120:40 =3 elephants in the same period of time.
Thus it takes them 2 hours to wash 4 elephants since the son washes 1 while his father washes 3.
POSTED BY IES CAMPANAR
AT THE CIRCUS
The most experienced trainer of a circus needs 40 minutes to wash an elephant, his son doing the same task in 2 hours. How long will it take them both to wash 4 elephants? How many elephants will each of them wash?
SOLUTION TO PUZZLE 2
In two hours the son washes one elephant while his father washes 120:40 =3 elephants in the same period of time.
Thus it takes them 2 hours to wash 4 elephants since the son washes 1 while his father washes 3.
Monday, 26 April 2010
FORTNIGHT'S PUZZLE 14
PUZZLE 14: 26th April - 2nd May (to be e-mailed by the 3rd May)
POSTED BY IES CAMPANAR
A CHESS GAME
There were 15 players in the latest chess game in which Kazimier Kaczyinski took part following the Swiss variant (all-against-all, once).The sum of all the points obtained by all the players except Kazimier was: 100 points. How many points did Kazimier get?
Note: 1 point for a win and ½ for a draw, each player.
SOLUTION
First of all we can argue that each person plays against the other 14 players, so the number of games should be 15x14. However, if we do it this way, each game is counted twice. This is why the total number of games is actually (15x14)/2 = 105.Since each game means 1 point of the total amount, we would have as a result 105 points.Consequently Kazimier got 105 – 100 = 5 points.
POSTED BY IES CAMPANAR
A CHESS GAME
There were 15 players in the latest chess game in which Kazimier Kaczyinski took part following the Swiss variant (all-against-all, once).The sum of all the points obtained by all the players except Kazimier was: 100 points. How many points did Kazimier get?
Note: 1 point for a win and ½ for a draw, each player.
SOLUTION
First of all we can argue that each person plays against the other 14 players, so the number of games should be 15x14. However, if we do it this way, each game is counted twice. This is why the total number of games is actually (15x14)/2 = 105.Since each game means 1 point of the total amount, we would have as a result 105 points.Consequently Kazimier got 105 – 100 = 5 points.
Monday, 12 April 2010
FORTNIGHT'S PUZZLE 13
PUZZLE 13: 12th-18th April (to be e-mailed by the 19th April)
POSTED BY IES CAMPANAR
ANIMALS
You have a fox, a chicken and a sack of grain. You must cross a river with only one of them at a time. If you leave the fox with the chicken he will eat it; if you leave the chicken with the grain he will eat it. How can you get all three across safely?
SOLUTION
Take the chicken over first. Go back and bring the grain next, but instead of leaving the chicken with the grain, come back with the chicken. Leave the chicken on the first side and take the fox with you. Leave it on the other side with the grain. Finally, go back over and get the chicken and bring it over.
POSTED BY IES CAMPANAR
ANIMALS
You have a fox, a chicken and a sack of grain. You must cross a river with only one of them at a time. If you leave the fox with the chicken he will eat it; if you leave the chicken with the grain he will eat it. How can you get all three across safely?
SOLUTION
Take the chicken over first. Go back and bring the grain next, but instead of leaving the chicken with the grain, come back with the chicken. Leave the chicken on the first side and take the fox with you. Leave it on the other side with the grain. Finally, go back over and get the chicken and bring it over.
Subscribe to:
Posts (Atom)
