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
Primary Mathematics World Contest (PMWC)
Do the math questions below and please write your answer in the comment form.
Question 1:
What is the greatest possible number one can get by discarding 100 digits, in any order, from the number 1234567891011121314151617…57585960
Question 2:
The larger circle has radius 12 cm. Each of the six identical smaller circles touches its two neighbours and the larger circle. What is the radius of the smaller circle ?
Question 3:
A group of 100 people consists of men, women and children (at least one of each). Exactly 200 apples are distributed in such a way that each man gets 6 apples, each woman gets 4 apples and each child gets 1 apple. In how many possible ways can this be done ?
Elementary Mathematics International Contest
Please read and then do carefully this math problems below:
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. Q2. 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.
