Fermat Mathematical Olympiad FMO is an annual competition developed and held by Fermat Education – an authorized Vietnamese organization board of many international Olympiad competitions. FMO is a mathematical playground for students from Kindergarten to high schoolers. Unlike other Mathematical Olympiad competitions, which have many difficult problems requiring complicated calculations or various formulae to be solved, FMO 2022 focuses on how students read, understand, and analyze the problems. As a friendly, accessible, and suitable competition for the majority of students, the examination questions of FMO 2022 will be arranged in increasing difficulty and composed relatively close to the curriculum framework. The tedious knowledge in textbooks is now vividly illustrated, thought-provoking, and in specific real-life settings. Students participating in FMO 2022 will be provided an opportunity to review the prior knowledge in a new approach, cultivate their passion for Mathematics and challenge themselves with real-world problems. Any student can participate in FMO 2022. as long as they have an interest in Mathematics and adequate basic mathematical knowledge. Ultimately, the purpose of this competition is to help every student answer the age-old question: “Why study Mathematics?”.
In 2022, Fermat Mathematical Olympiad FMO takes place for the third time. In the previous seasons, the competition was a great success by having attracted the attention of many students from all over the world such as Thailand, Philippines, Bulgaria, Indonesia, Turkey, India, …. Following that success, with some alterations in the examination structure and the appearance of real-life problems, together with many valuable cash prizes, FMO 2022 promises to be an educational, interesting but also challenging mathematical playground for students. This is also a great opportunity for the participants to compete on a global scale and have memorable experiences. (sc: Facebook Fermat Mathematical Olympiad)
A. Warm-up (4 points per question / No points deducted for wrong answers)
1. Given 4 figures below, which figure should come next?
A)
B)

C)

D)

E)
2. Which number should be filled in the blue circle so that all calculations following the arrows are correct?

A) 43
B) 45
C) 25
D) 53
E) 35
3. A baby wants to take the milk bottle in the 8th stair. Each stair takes him 1 second to climb up and 1 second to climb down. He climbs up 3 stairs and climb down 1 stair. He keeps doing that until he gets the milk bottle. How long does it take him in total?

A) 8 seconds
B) 16 seconds
C) 12 seconds
D) 10 seconds
E) 14 seconds
4. Teacher gave Victoria’s class homework to draw an animal. Victoria drew a bird as below. How many triangles are there in Victoria’s picture?

A) 13
B) 14
C) 15
D) 16
E) 17
5. Mr. Simon grows carrots in his square garden. He wants to have 2 carrots in each column and each row. How many carrots Mr. Simon need to be harvest?

A) 2
B) 3
C) 1
D) 5
E) 4
B. Speed-up (6 points per question / No points deducted for wrong answers)
6. There are 5 routes from A to B as the map below. Can you arrange these 5 routes in order from the longest to the shortest?

A) yellow, blue, green, black, red
B) black, red, blue, yellow, green
C) red, black, green, yellow, blue
D) red, black, green, blue, yellow
E) None of the above
7. Lexie has $26. She wants to buy 3 apples and some pears. An apple costs$5 and a pear costs \$2. At most how many pears can Lexie buy?
A) 3
B) 7
C) 4
D) 6
E) 5
8. In a festival, five people take part in a hot dog eating contest. The table below shows the number of hot dogs eaten by each person. Who ate 15 hot dogs?
A) Meredith
B) Christina
C) Owen
D) Jo
E) Mark
9. A rubik is made up of 64 little equal-sized cubes. Each face is painted by a different colour. How many little cubes are not covered by green or red?

A) 16
B) 32
C) 34
D) 36
E) 28
10. Five couples: 5 men and 5 women joined a running race. The result of each person is recorded as the table below. After that, the judge gave a prize to a couple whose the total running time is the least. Which couple got the prize?
A) Ben, Bailey
C) Shane, Stephanie
D) Alex, Izzie
E) Jackson, April
C. Challenge (8 points per question / No points deducted for wrong answers)
11. We have a magic square as below. The sum of each row is on the right and the sum of each column is at the bottom. Find the missing number.
A) 12
B) 13
C) 14
D) 15
E) 16
12. Andrew has 26 balloons. He wants to give all balloons to his 5 friends: Addison, Burke, Callie, Erica, George such that the number of balloons for each friends is different and each friend gets at least 3 balloons. What can be the greatest number of balloons Erica can get?

A) 6
B) 7
C) 8
D) 9
E) 10
13. Given 4 logs with the length below. Uncle John wants to cut the woods so that they all have the same length. At least how many cm long does he have to cut down in total?

A) 112cm
B) 177cm
C) 65cm
D) 36cm
E) 149cm
14. According to the pattern shown, how many cubes are there in the 7th group?

A) 16
B) 64
C) 36
D) 49
E) 55
15. Teddy has 4 boxes of candies. The number of candies in each boxes are 6, 6, 9 and 10. Teddy chooses 3 boxes and eats one candy from each of them. He stops eating when he can no longer do that. What is the least number of candies that are left?
A) 0
B) 1
C) 2
D) 3
E) 4