The Southeast Asia Mathematical Olympiad (SEAMO) is an international Math Olympiad competition that originated in Singapore and was founded by Mr. Terry Chew in 2016 in 8 Southeast Asian Countries. Since then, it is growing its popularity around the world. In 2019 it was recognized by 18 countries. In 2020 total number of participating countries increased to 22, including students from Indonesia, Brazil, China, Newzealand, and Taiwan students enrolled in SEAMO 2022-23.

**Problem and Solution SEAMO 2016 paper C**. Soal ini bersumber dari seamo-official.org

1. Find the value of

\(100 − 98 + 96 − 94 + ⋯+ 8 − 6 + 4 − 2\)

(A) 46

(B) 48

(C) 50

(D) 52

(E) 54

2. The missing number in the following (E) None of the above sequence is _____.

\(4, 6, 10, 14, 22, 26, 34, ( ) , 46…\)

(A) 36

(B) 37

(C) 38

(D) 39

(E) 40

3 . In the pentagon below, AB = BC = CD = DE = EF . Find \(∠y\)

(A) 106°

(B) 108°

(C) 110°

(D) 112°

(E) None of the above

4. Mr. Wang met with heavy traffic on the expressway. As a result, the speed of his car was reduced by 20%. What was the percentage increase in time taken for his journey?

(A) 10%

(B) 15%

(C) 20%

(D) 25%

(E) None of the above

5. Find the number of ways in which you could travel from point A to point B by passing through point X in the diagram shown below. You can only move in the → and ↑ directions.

(A) 16

(B) 17

(C) 18

(D) 19

(E) None of the above

6. Jane forgot her pencil case when she walked to school. So her brother cycled to give it to her. After receiving it, she took another 4 more minutes to reach school. Her brother reached home at the same time. If cycling is 3 times faster than walking, how many minutes did Jane take to walk to school from home?

(A) 14

(B) 16

(C) 18

(D) 20

(E) None of the above

7. Two dice are rolled at the same time. What is the chance that the sum of the 2 numbers on the up faces is 8?

(A) \(\frac{1}{6}\)

(B) \(\frac{1}{9}\)

(C) \(\frac{1}{12}\)

(D) \(\frac{5}{36}\)

(E) \(\frac{7}{36}\)

8. A bag contains 8 red, 7 white, 5 yellow, 3 blue and 2 black balls. Without looking Roy takes out the balls one by one. What is the least number of balls he must take out so that, for certain, he will have at least 4 balls of the same colour?

(A) 11

(B) 12

(C) 13

(D) 14

(E) None of the above

9. The average age of \(m\) number of teachers and \(n\) number of engineers are 32 and 40, respectively. The average age of the same group of teachers and engineers is 35. Find \((m + n)\).

(A) 4

(B) 6

(C) 8

(D) 10

(E) None of the above

10. A fast food outlet sells chicken nuggets in boxes of either 4 or 7. What is the largest number of nuggets that one cannot buy?

(A) 11

(B) 17

(C) 19

(D) 22

(E) None of the above

11. The figure below shows 3 squares and two circles. Find the area of the smallest square in cm².

(A) 46

(B) 47

(C) 48

(D) 49

(E) None of the above

12. In the number line shown below, \(2a = 3b – 8\). Find the value of \((2c + d)\).

(A) 15

(B) 16

(C) 17

(D) 18

(E) None of the above

13. Find the value

\(\frac{1}{2}+\frac{1}{2×2}+\frac{1}{2×2×2}+…+\frac{1}{2×2×2×2×2×2×2×2}\)

A. \(\frac{56}{128}\)

B. \(\frac{127}{128}\)

C. \(\frac{128}{256}\)

D. \(\frac{255}{256}\)

E. None of the above

14. In ΔABC, points D,E and F are midpoints of CE,AF and BD respectively. It is known the area of ΔABC is 56 cm². Find the area of ΔDEF.

(A) 5

(B) 6

(C) 7

(D) 8

(E) None of the above

15. Find the 2016th digit after the decimal in \(\frac{5}{7}\)

(A) 1

(B) 2

(C) 4

(D) 5

(E) 7

16. Let \(r, s, t, u\) be whole numbers. If \(2^r × 3^s × 5^t × 7^u = 252\), then what does \(r+2s+3t+4u\) equal to?

(A) 4

(B) 6

(C) 8

(D) 10

(E) None of the above

17. Find the number of triangles that can be formed by using any 3 points as their vertices.

(A) 20

(B) 25

(C) 30

(D) 35

(E) None of the above

18. Evaluate

\(\frac{2016}{2016^2 – 2015×2017}\)

(A) 1

(B) 2015

(C) 2016

(D) 2017

(E) None of the above

19. John cut away one sixth of a pizza. He realized the curved circumference of the remaining pizza is 15π . What was the diameter of the pizza in inches?

(A) 10

(B) 12

(C) 14

(D) 16

(E) 18

20. There are 200 kilograms of oatmeal in a supermarket. On the \(1^{st}\) day, \(\frac{1}{2}\) of the oatmeal was sold. On the \(2^{nd}\) day, \(\frac{1}{3}\) of the remaining oatmeal was sold. On the \(3^{rd}\) day, \(\frac{1}{4}\) of the remaining oatmeal was sold. This pattern went on until on the \(199^{th}\) day, \(\frac{1}{200}\)of the remaining oatmeal was sold. Find the amount of oatmeal, in kilograms, the was left.

(A) 1

(B) 2

(C) 3

(D) 4

(E) None of the above

21. Aloysius, Barry, Carl, Dylan and Edward are participating in an international chess competition where each contestant must play exactly one game against each other.

Aloysius played 4 games.

Barry played 3 games.

Carl played 2 games.

Dylan played 1 game.

How many games has Edward played so far?

22. The digits below can form 24 different fourdigit numbers. Find the average of these 24 numbers.

2, 5, 7 and 8

23. The figure shows 2 blue circles and 3 blue semicircles, all of identical radii, inscribed in a big semicircle. Find the ratio of the area of the big semicircle to the area of the area of the blue regions.

24. The following four-digit numbers are similar to each other in some ways.

1383 1996 1231

Firstly, they all start with 1. Secondly, there are 2 identical digits in each number. How many such numbers are there?

25. A triangle can be formed with sides of lengths 3, 4 and 5. It is impossible, however, to construct a triangle with sides of lengths 3, 4, and 7. Jane has 8 sticks, each stick having different lengths, which are whole numbers. She observes that she cannot form a triangle using any 3 sticks as the sides. What is the shortest possible length of the longest stick Jane has in cm?