SOAL MASMO OLIMPIADE SAINS DAN MATEMATIKA MALAYSIA

Soal Masmo (Olimpiade Sains dan Matematika Malaysia) sebagai berikut:

1. A family consists of father, mother, and some children. The average age of the family is 20 years. Without the 40-year-old father, the average age of the family decreases to only 16 years. How many children are there in the family?
2. In a football league with 7 teams (A, B, C, D, E, F, and G), each team plays each other team exactly once. So far, A has played onematch, B has played 2 matches, C has played 3 matches, D has played 4 matches, and E has played 5 matches, and F has played 6 matches. How many matches has G played so far?
3. How many 8-digit numbers composed only of 1, 2, and 3 exist, in which any two neighbouring digits differ by 1?
4. The last digit of a three-digit number is 4. If we move the last digit to the front, the number is reduced by 99. What is the sum of digits of the original number?
5. Let S be the least number with the following property: 10 x S is a perfect square and 6 x S is a perfect cube. Find sum of the digits of the number S?
6. On the island of nobles and liars, 37 people are standing in a queue. Everyone, except the first person in the queue, said, that the person before him in the queue is a liar. The first man in the queue, said, that all people, standing after him are liars. How many liars are in the queue? (Nobles always speak the truth, and liars always tell lies.)
7. What is the degree-measure of the interior angle between the hour and minute hands at 7:50 pm?
8. A palindrome is a positive integer that is the same when read forwards or backwards. For example, three palindromes are 8; 343 and 5578755. Determine the number of palindromes less than 500?
9. How many right-angled triangles can be formed by joining three vertices of a given regular 8-gon?
10. How many rectangles are in this picture?
    

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