INTERNATIONL MATHEMATICS AND SCIENCE OLYMPIAD FOR PRIMARY SCHOOLS (IMSO) 2006
1. The solution to each clue of this crossnumber is a two-digit number. None of these numbers begins with zero. Complete the crossnumber, stating the order in which you solved the clues and explaining why there is only one solution.
Clues Across
1. A square number
3. A multiple of 11
Clues Down
1. A multiple of 7
2. A cube number
2. Notice that 2^2 + 2^2 = 23 , so two squares can sum to give a cube; however, the two squares here are equal (to 4).
(a) Find two unequal squares whose sum is a cube.
(b) Show that there are infinitely many pairs of unequal squares whose sum is equal to a cube.
Note: ^ means square
Math Olympiad in Taiwan (IMSO)
Short Answer: there are 20 questions, fill in the correct answers in the answer
sheet. Each correct answer is worth 2 points. Time limit: 60 minutes.
1. In the 5×5 square the numbers 1, 2, 3, 4 and 5 are arranged in such a way that every number occurs precisely once in each column. In the 5×5 square shown, what is the entry in the position marked with * ?
2. The length of the sides of a triangle PQR are PQ=5, QR=3 and RP=4. The bisectors of the angles P and Q meet at the point I. What is the area of the triangle PQI?
Primary Mathematics World Contest
We have primary mathematics world contest problems for individual contest and may be usefull for your students.
1. There are four kinds of dollar-notes (or dollar-bills) of value $1, $5, $10, and $50 respectively. There is a total of nine dollar-notes, with at least one dollar-note of each kind. If the total value of these dollar-notes is $177, how many $10 dollar-notes are there ?
2. A bus starts from town A to town B and another bus starts from town B to town A on the same road. They run with constant speed to their destinations and back home without stopping. The buses pass by each other for the first time at 700 km (kilometers) from town A and they pass by each other for the second time on the way back at 400 km from town B. How many km is it from town A to town B?
3. A contractor requests 2 men to build brick walls. One man can build a brick wall in 9 hours, while the other man can do the same job in 10 hours. However, when the two men work together, there will be shortfall of a total of 10 bricks per hour, and it takes them exactly 5 hours to complete the brick wall . Find the total number of bricks used on the wall.
4. Clock A is ten seconds faster than standard time every hour. Clock B is twenty seconds slower than the standard time every hour. If we adjust the two clocks to standard time at the same time, then within 24 hours Clock A shows 7:00 while Clock B shows 6:50. What is the standard time at that moment ?
