Farm Animals Three countrymen met at a cattle market. "Look here," said Hodge to Jakes, "I'll give you six of my pigs for one of your horses, and then you'll have twice as many animals here as I've got."
"If that's your way of doing business," said Durrant to Hodge, "I'll give you fourteen of my sheep for a horse, and then you'll have three times as many animals as I."
"Well, I'll go better than that," said Jakes to Durrant; "I'll give you four cows for a horse, and then you'll have six times as many animals as I've got here."
No doubt this was a very primitive way of bartering animals, but it is an interesting little puzzle to discover just how many animals Jakes, Hodge, and Durrant must have taken to the cattle market.
In the product shown below, the letters F and L represent different digits from 0 to 9. Determine the value of F and of L.
Area Problems
Problem 1 - Find the area of the shaded region.
Rugby As any rugby fan will know, a frustrating aspect of the sport is that when you see a score it is not always clear what has been scored. This situation is down to the points system:
·3 points for a penalty kick or drop goal ·5 points for a try ·7 points for a try and a conversion For example, if a team has 21 points, this could be three tries and three conversions. Or seven penalty kicks.
Here’s the question: 1) What is the highest rugby score that can be made with only one possible combination of penalties, tries and conversions? In other words, if a team scores this amount you know exactly the breakdown of what was scored. And if they score any higher, you don’t.
And two more questions for fun: 2) What is the highest rugby score that can be made in at most two combinations of penalties, tries and conversions?
3) What is the highest rugby score that can be made in at most three combinations of penalties, tries and conversions?
And a bonus question, if you thought those were too easy. What is the highest rugby score that can be made in at most 49 ways?
The coin and the chessboard A coin of diameter 1 is thrown on an infinitely large chessboard with squares of side 2. What is the chance that the coin lands on a position touching both black and white?