Flight of Stair Problems

2018 25 A flight of stairs has 9 steps. David can go up for 1 step or 2 steps each time. The 5th
Final step cannot be stepped on as it is destroyed. How many way(s) is / are there for David
to go up the stairs?
2019 21 A flight of stairs has 9 steps. Alice can go up for 1 step, 2 steps or 3 steps each time.
Semi The 4th step cannot be stepped on as it is destroyed. How many way(s) is / are there
for Alice to go up the stairs?
2019 27 A flight of stairs has 9 steps. Alice can go up for 1 step or 2 steps each time. The 6th
Final step cannot be stepped on as it is destroyed. How many way(s) is / are there for Alice
to go up the stairs?
2020 17 A flight of stairs has 10 steps. Peter can go up for 1 step or 3 steps each time. How
Heat many way(s) is / are there for Peter to go up the stairs?
2020 22 A flight of stairs has 9 steps. Peter can go up for 1 step, 2 steps or 3 steps each time.
Semi How many way(s) is / are there for Peter to go up the stairs?
2021 21 A flight of stairs has 10 steps. Andy can go up for 1 step or 2 steps each time. How
Heat many way(s) is / are there for Andy to go up the stairs?
2021 24 A flight of stairs has 10 steps. Peter can go up for 1 step, 2 steps or 3 steps each time.
Semi How many way(s) is / are there for Peter to go up the stairs?
2022 23 A flight of stairs has 11 steps. David can go up for 1 step, 2 steps or 3 steps each time.
SEMI How many way(s) is / are there for David to go up the stairs?
2022 27 A flight of stairs has 8 steps. Bonny can climb up 1 step or 2 steps at a time. In how
FINAL many different way(s) can Bonny climb up the stairs?
Eg A flight of stairs has 14 steps. Peter can go up for 1 step or 3 steps each time. 6th step
is destroyed. How many way(s) is / are there for Peter to go up the stairs?
Pigeon Hole Problems
2018 23 At least how many of 169 children that were born in the same Chinese zodiac year?
Heat (There are 12 different Chinese zodiac years)
2019 19 In a primary school, at least how many of 111 students that are in the same grade?
Heat
2019 23 In a secondary school, at least how many of 380 students that are in the same grade?
Semi
2020 18 It is known that there are 5 classes of grade 5 in a primary school, at least how many of
Heat 246 grade 5 students who are in the same class?
2020 23 It is known that there are 7 classes of grade 5 in a primary school, at least how many of
Semi 366 grade 5 students who are in the same class?
2021 18 It is known that there are 6 grade 5 classes in a primary school. There are 173 students
Heat in total. At least how many student(s) are there in the class with most students?
2021 22 It is known that there are 8 classes of grade 5 in a primary school and there are 392
Semi grade 5 students. There would be at least one student in each class. In the class with
most students, at least how many student(s) is / are there in the same class?
Combinations and Permutations
2018 22 Five students join a competition. Only top 3 students can get an award. How many
Heat different way(s) of getting awards is / are there?
2019 18 10 students join a competition. Only top 5 students can advance to next round. How
heat many different way(s) of advancing is / are there?
2019 22 12 students join a competition. Only top 4 students can advance to next round. How
Semi many different way(s) of advancing is / are there?
2020 21 17 students join a competition. Only top 3 students can be promoted to next round.
Semi How many different way(s) of promotion advance is / are there?
2021 19 9 students join a competition. Only top 4 students can advance to next round. How
Heat many different way(s) of advancing is / are there?
2021 21 15 students join a competition. Only top 5 students can be promoted to next round.
Semi How many different way(s) of promotion advance is / are there?
2020 18 Now Mary and Charlie and 6 children stand as a row. If Mary and Charlie cannot stand
Heat at the end of the row, how many arrangement(s) is / are there?
2020 28 Now Mary and Charlie and 6 children stand as a row. If Mary and Charlie cannot stand
Final at the end of the row, how many arrangement(s) is / are there?
2020 27 16 students join a competition. Only top 4 students can be promoted to next round.
Final How many different way(s) of promotion advance is / are there?
Eg There are 8 types of ice-creams at an ice-cream shop. If randomly picking up 3 types,
how many different combination(s) is / are there?
Eg Pick 5 from 12 children to take part in mathematics competition. How many different
combination(s) is / are there?
2020 28 Now Mary and Charlie and 6 children stand as a row. If Mary and Charlie cannot stand
Final at the end of the row, how many arrangement(s) is / are there?
2021 25 Now Mary and Charlie and 5 children stand as a row. If Mary and Charlie cannot stand
Final at the beginning or the end of the row, how many arrangement(s) is / are there?
2020 25 Choose 3 digits from 1, 2, 3, 4, 6, 8 and 0 to form 3-digit numbers. How many even
Semi number(s) greater than 400 is / are there? (The repetition of digits is not allowed)
2020 26 Choose 3 digits, without repetition, from 1, 3, 4, 5, 6, 8 to form 3-digit numbers. How
Final many number(s) can be divisible by 4?
2020 29 Choose 3 digits from 0, 1, 3, 5, 7 and 9 to form 3-digit numbers. How many odd
Final number(s) greater than 333 is / are there? (The repetition of digits is not allowed)
2021 23 Choose 3 digits from 1, 2, 3, 4, 6, 8 and 0 to form 3-digit numbers. How many even
Semi number(s) greater than 300 is / are there? (The repetition of digits is not allowed)
2021 27 Choose 3 digits from 0, 1, 3, 5, 7 and 9 to form 3-digit numbers. How many odd
Final number(s) greater than 111 is / are there? (The repetition of digits is not allowed)

2018 25 If Alice goes from point A to point B, each step can only move up or move right. How
heat many way(s) is / are there?
2018 30 If Andy goes from point A to point B, each step can only move following the direction
Final of arrows. How many way(s) is / are there?

2019 25 If Alice goes from point A to point B, each step can only move up or move right. How
Semi many way(s) is / are there?

2019 29 If Alice goes from point A to point B, each step can only move up or move right. How
Final many way(s) is / are there?
 Eg If Andy goes from point A to point B, each step can only move up or move right. How
many way(s) is / are there?

Eg

eg

Pigeon Holes Problems

2018 24 Numbers are drawn from 55 integers 1 to 55. At least how many number(s) is / are
Heat drawn at random to ensure that there are two numbers whose sum is 24?
2019 20 Numbers are drawn from 61 integers 10 to 70. At least how many number(s) is / are
Heat drawn at random to ensure that there are two numbers whose sum is 30?
2019 24 Numbers are drawn from 80 integers 20 to 99. At least how many number(s) is / are
Semi drawn at random to ensure that there are two numbers whose sum is 70?
2020 20 Numbers are drawn from 70 integers 15 to 84. At least how many number(s) is / are
Heat drawn at random to ensure that there are two numbers whose sum is 62?
2020 24 Numbers are drawn from 90 integers 10 to 99. At least how many number(s) is / are
Semi drawn at random to ensure that there are two numbers whose sum is 75?
2020 25 Numbers are drawn from 99 integers 20 to 118. At least how many number(s) is / are
Final drawn at random to ensure that there are two numbers whose sum is 154?
2021 17 Numbers are drawn from 50 integers 12 to 61. At least how many number(s) is / are
Heat drawn at random to ensure that there are two numbers whose sum is 42?
2018 29 Numbers are drawn from 65 integers 1 to 65. At least how many number(s) is / are
Final drawn at random to ensure that there are two numbers whose difference is 14?
 Passing Balls
2018 28 There are 5 students passing the balls in an order. Andy holds the ball first. After 4-
Final time pass, Charles holds the ball now. How many way(s) is / are there?
2019 25 Andy is passing ball with 4 friends. Andy holds the ball in the beginning. After 5 passes,
Final David holds the ball. How many way(s) is / are there passing the ball?
2021 26 Andy is passing ball with 3 friends. Andy holds the ball in the beginning. After 6 passes,
Final David holds the ball. How many way(s) is / are there passing the ball?
Emma is playing a ball-passing game with 4 friends: Frank, Grace, Henry, and Ivy.
Emma starts with the ball. After 5 passes, Ivy holds the ball. How many way(s) are
there to pass the ball?
Five children — Noah, Olivia, Paul, Quinn, and Riley — are standing in a line. Noah
starts with the ball. The ball is passed exactly 6 times, and Riley has it at the end. The
ball can only be passed to someone next to the current holder. How many such passing
sequences are possible?
Chickens And Rabbits Problems
2018 26 Andy has 16 $5 and $10 coins altogether. He has $105 in total. How many $10 coin(s)
Final does he have?
2019 30 Andy has 15 $2 coins and $5 coins in total $54. How many $5 coins does Andy have?
Final
2022 30 Bob has 30 $2 coins and $5 coins in total $87. How many $5 coin(s) does Bob have?
Final
Non Routine Problems
2020 19 It is given that an apple weighs 100g, an orange weighs 80g and an egg weighs 40g.
Heat How many combination(s) is / are there such that the total weight is exactly 400g?
2018 27 There are 40 students in Grade 5. 23 and 25 students like playing basketball and
Final volleyball respectively. 2 students like none of the ball games. Find the number of
students who like both ball games.
There are 60 students in Grade 5. 35 students join music class. 38 students join
painting class. 3 students do not join any classes. How many students join both of the
classes?
Triangle Inequality Theorem
2022 18 Amy draws all triangles which perimeter is 15cm and lengths of sides are integers. How
Heat many different types of triangle(s) does she draw? (Triangles with sides (5,5,6) and
(5,6,5) are regarded as the same type of triangle)
2018 21 1. Amy draws all triangles which perimeter is 17cm and length of sides are integers.
Heat How many different types of triangle(s) does she draw? (Triangles with sides (5,5,6)
and (5,6,5) are regarded as the same type of triangle)
2019 17 Alice draws all isosceles triangles whose perimeter is 40cm and length of sides are
Heat integers. How many different types of triangle(s) does she draw?
2022 29 Annie draws all isosceles triangles whose perimeter is 50cm and length of sides are
Final integers. How many different triangle(s) does she draw?