If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?
A garrison of 600 men has just enough bread ... but, with the news that the enemy was planning an attack... How many ounces of bread a day must each man in the garrison be allowed, to hold out 45 days against the siege of the enemy?
In a race the odds are: 2 to 1 against the rhinoceros winning and 3 to 2 against the hippopotamus winning. What are the odds against the elephant winning if the race is fair?
At Caesar's Palace in Vegas, were three poker players - Alan, Bernie and Craig. At the beginning of the night the amount of money each had was in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of the players won 1 200. Suppose at the outset they had a, b and c.
This solution was sent to you by Prav Idaikkadar and Sheli Levenson (YR9) of the North London Collegiate School Maths Puzzle Club. Have a nice day
a : b: c = 7 : 6 : 5 = 7/18 : 6/18 : 5/18 6 : 5 : 4 = 6/15 : 5/15 : 4/15 The lowest common multiple of 15 and 18 is 90. This is 35/90 : 30/90 : 25/90 36/90 : 30/90 : 24/90 We can see that Craig lost 1/90 of his money and Alan gained it. We are told that the sum of money gained is 1,200. Therefore 1/90 of the money = 1,200. The total amount of money is 90 * 1,200 = 108,000. In the beginning of the game Alan had 35/90 of the total money 35/90 * 108, 000 = 42, 000. Bernie had 30/90 of the total money and this is 30/90 * 108, 000 = 36, 000. Craig had 25/90 of the total money and this is 25/90 * 108, 000 = 30, 000. These were the assets of the players at the beginning of the evening
The lowest common multiple of 15 and 18 is 90.
This is 35/90 : 30/90 : 25/90
36/90 : 30/90 : 24/90
We can see that Craig lost 1/90 of his money and Alan gained it. We are told that the sum of money gained is 1,200. Therefore 1/90 of the money = 1,200.
The total amount of money is 90 * 1,200 = 108,000.
In the beginning of the game Alan had 35/90 of the total money
35/90 * 108, 000 = 42, 000.
Bernie had 30/90 of the total money and this is
30/90 * 108, 000 = 36, 000.
Craig had 25/90 of the total money and this is
25/90 * 108, 000 = 30, 000.
These were the assets of the players at the beginning of the evening
Well done Prav and Sheli. Other very good solutions were sent in by Elizabeth Wells, also from the N.C.L.S. puzzle club and James Page from Hethersett High School, Norwich.