Individual Math Contest
Time limit: 90 minutes
-Write down your name, team name and candidate number on the answersheet.
-Write down all answers on the answer sheet. Only Arabic NUMERICALanswers are needed
- Answer all 15 problems. Each problem is worth 1 point and the total is 15points.
- For problems involving more than one answer, points are given only when
- ALL answers are corrected.
- No calculator or calculating device is allowed.
- Answer the problems with pencil, blue or black ball pen.
- All materials will be collected at the end of the competition.
1. Starting from the central circle, move between two tangent circles. What is the number of ways of covering four circles with the numbers 2, 0, 0 and 8 inside, in that order?
2. Each duck weighs the same, and each duckling weighs the same. If the total weight of 3 ducks and 2 ducklings is 32 kilograms, the total weight of 4 ducks and 3 ducklings is 44 kilograms, what is the total weight, in kilograms, of 2 ducks and 1 duckling?
3. If 25% of the people who were sitting stand up, and 25% of the people who werestanding sit down, then 70% of the people are standing. How many percent of the people were standing initially?
4. A sedan of length 3 metres is chasing a truck of length 17 metres. The sedan is
travelling at a constant speed of 110 kilometres per hour, while the truck is travelling at a constant speed of 100 kilometres per hour. From the moment when the front of the sedan is level with the back of the truck to the moment when the front of the truck is level with the back of the sedan, how many seconds would it take?
5. Consider all six-digit numbers consisting of each of the digits ‘0’, ‘1’, ‘2’, ‘3’, ‘4’ and ‘5’ exactly once in some order. If they are arranged in ascending order, what is the 502nd number?
* Write down your name and country on every page.
* Answer all 6 questions.* You have 120 minutes to work on this test.
* Write down your answer on the provided answer sheets.
1. We are given a number of equilateral triangles with lateral length 1 cm. They come in two colors, yellow and blue. Three blue and one yellow triangles can be arranged to make an equilateral triangle of lateral size 2 cm (see 1st Pattern below). Six blue and three yellow triangles are arranged to form an equilateral triangle of lateral size 3 cm (see 2nd Patternbelow).
a. How many blue triangles and yellow triangles are required in the arrangement with lateral length 6 cm?
b. If you would like to make a similar arrangement to form an equilateral triangle of lateral size 10 cm, how many blue triangles and yellow triangles are needed?
c. If you would like to make equilateral triangle of lateral size 20 cm, how many blue triangles and yellow triangles are needed?
Time Limit – 90 Minutes 10th September 2004 Lucknow, India
Team _________________ Contestant No. ____________
1. There are 5 trucks. Trucks A and B each carry 3 tons. Trucks C and D each carry 4.5 tons. Truck E carries 1 ton more than the average load of all the trucks. How many tons does truck E carry?
2. Let A = 200320032003 2004200420042004 and B = 200420042004 2003200320032003.
Find A – B.
3. There are 5 boxes. Each box contains either green or red marbles only. The numbers of marbles in the boxes are 110, 105, 100, 115 and 130 respectively. If one box is taken away, the number of green marbles in the remaining boxes will be 3 times the number of red marbles. How many marbles are there in the box that is taken away?
4. Find the smallest natural number which when multiplied by 123 will yield a product that ends in 2004.