Enigma+of+the+month

This contest is opened to everyone. Email me your answers at cbabulaud@isparis.edu An award ceremony will be held at the end of the school year.

February Grades 6-8 One of your friends is heading north for a holiday and the other friend is heading south. If their holiday destinies are 1029 miles apart and one car is travelling at 45 miles per hour and the other car is travelling at 53 miles per hour. How many hours before the two cars pass each other? Grades 9-12 A man's flight was delayed. While waiting for his flight, he decided to calculate the speed of one of the electronic walkways in the airport. He first walked in the direction of the walkway and reached the end in a minute. The he walked in the opposite direction and was slowed down so that he reached the end in 3 minutes. How long will it take him to cover the distance of the walkway if it did not work?

November Grades 6-8 One of your friends is heading north for a holiday and the other friend is heading south. If their destinies are 1029 miles apart and one car is travelling at 45 miles per hour and the other car is travelling at 53 miles per hour. How many hours before the two cars pass each other? Grades 9-12 An air-plane flies against the wind from A to B in 8 hours. The same air-plane returns from B to A in the same direction as the wind in 7 hours. Find the ratio of the speed of the air-plane (in still air) to the speed of the wind.

October Grades 6-8

Parents donated fudge for the fundraiser for your classroom. 40 pounds of chocolate fudge sold for $2.15 per pound and vanilla fudge sold for $1.90 per pound. Your class made $156.20. How many pounds of fudge were sold? Grades 9-10 Allie has an income which is five eighths that of Basil. Allie's expenses are one-half those of Basil and Allie saved 40% of his income. What is the percentage of his income that Basil saves.

June Grades 6-8 Justin is making snowballs to build a fort on the winter break. Justin can build 15 snowballs in an hour but 2 snowballs melt every 15 minutes. How long will it take him to build 210 snowballs? Grades 9-12 A van travels a maximum of 100 km/h. Its speed decreases in proportion with the number of passengers. The van can carry a maximum of seven people. Given that the van can travel 88 km/h with 3 people in the van, what will be the speed of the van when 6 people are on board?

April Grades 6-8 5 hockey pucks and 3 hockey sticks cost $23. 5 hockey pucks and 1 hockey stick cost $20. How much does one hockey puck cost? Grades 9-12 A right angled triangle in the first quadrant is bounded by lines y = 0, y = x, and y = -x + 5. Find its area.

March Grades 6-8 The Adams family was going to buy a car for $5800. The car dealer offered the Adams family two options for buying the car. They could pay the full amount in cash, or they could pay $1000.00 down and $230.00 a month for 24 months on the installment plan. How much more would they pay for the car on the installment plan? Grades 9-8 A van travels a maximum of 100 km/h. Its speed decreases in proportion with the number of passengers. The van can carry a maximum of seven people. Given that the van can travel 88 km/h with 3 people in the van, what will be the speed of the van when 6 people are on board?

October Grades 6-8 When the Birthday cake was about to be served, you were told you could have 0.6, 60%, 3/5, 6%. Which 3 will give you the same size portions? Grades 9-12 A student at St. F. X. decided to become his own employer by using his car as a taxi for the summer. It costs the student $693.00 to insure his car for the 4 months of summer. He spends $452.00 per month on gas. If he lives at home and has no other expenses for the 4 months of summer and charges an average of $7.00 per fare, how many fares will he have to get to be able to pay his tuition of $3280.00?

**__February__** **Grades 6 - 8**

**Grades 9 - 12** Father John and mother Ursula have two daughters Emma and Caroline. Caroline is twice as old as Emma, Ursula is four times as old as Caroline, and John is five years older than Ursula. Together, they are 100 years old. How old is father John?

**__January__** **Grades 6 - 8** It is possible to start at the top left hand corner, move one square to a 1, then move two squares to a 2, then move three squares to a 3, and so on, without revisiting any square, and ending with the 8 in the bottom right hand corner. Moves can be made only vertically or horizontally, not diagonally. See if you can find such a route.
 * = **Start** ||= . 1 . ||= . 3 . ||= . 2 . ||= . 5 . ||= . 4 . ||= . 4 . ||= . 6 . ||
 * = 2 ||= 4 ||= 5 ||= 3 ||= 4 ||= 6 ||= 7 ||= 4 ||
 * = 5 ||= 2 ||= 3 ||= 5 ||= 3 ||= 5 ||= 6 ||= 5 ||
 * = 4 ||= 3 ||= 6 ||= 3 ||= 5 ||= 4 ||= 7 ||= 4 ||
 * = 3 ||= 4 ||= 7 ||= 6 ||= 5 ||= 7 ||= 6 ||= 5 ||
 * = 5 ||= 6 ||= 5 ||= 3 ||= 7 ||= 6 ||= 4 ||= 7 ||
 * = 4 ||= 7 ||= 4 ||= 5 ||= 6 ||= 5 ||= 5 ||= 7 ||
 * = 6 ||= 5 ||= 7 ||= 7 ||= 5 ||= 6 ||= 4 ||= **8** ||

**Grades 9 - 12** This enigma has nothing to do with George Orwell! (a) Did you know that 1985²– 1984² is a perfect square? When did this last happen? (b) It is not very difficult to express 1984 usinf eight "4" digits and any mathematical symbols you might care to use, but it will tax your ingenuity to do the same using four "8" digits.

**__December__** **Grades 6 - 8** The square number 25 has the property that when its digits are increased by 1 it is converted to 36 another square number. (2 + 1 = 3 and 5 + 1 = 6) There is just one 4-digit square number with the same property. What is it?

**Grades 9 - 12** Tom, Dick and Harry engage in some track and field events in which points are awarded for 1st, 2nd and 3rd. At the end of the events, Tom has 22 points, while Dick and Harry both have 9 points. No-one else had any points. Dick was 1st in the javelin throw. Who came 2nd in the 100 meters?

**__November__** **Grades 6 - 8** Solve the following anagrams, which are either mathematical terms or names of famous mathematicians.
 * fiyintin
 * artiducqa
 * tessardes
 * zirpetuma

**Grades 9 - 12** D. St P. Barnard regularly sets puzzles in //The Daily Telegraph// and set one based on the intriguing relation (6048 + 1729)² = 60481729. There is only one other pair of 4-digit numbers with the same property. However similar properties exist for pairs of single-digit numbers and pairs of 2-digit numbers. Investigate all the solutions to (//a// + //b//)² = //ab// where //ab// is a 2-digit number, and (//ab// + //cd)//² = //abcd// where //abcd// is a 4-digit number.