Question 1
Jane plans to go on a holiday from 22 July (first day) to 3 September (last day). How many days is she planning to spend on her holidays?
AMO 2027 Grades 2-3 SET 9 - Self-study
Question 2
John wrote a 4-digit number on a paper and asked Peter to guess the number.
• Peter asked, “Is the number 1234?”
• John replied, “One of the digits is correct, the position of that digit is also correct.”
• Peter asked again, “Is the number 5167?”
• John replied, “Two digits are correct, but the positions of these two digits are wrong.”
• Peter asked again, “Is the number 8691?”
• John said, “All four digits are correct, but the digits are all in the wrong places.”
What is the number written by John?
• Peter asked, “Is the number 1234?”
• John replied, “One of the digits is correct, the position of that digit is also correct.”
• Peter asked again, “Is the number 5167?”
• John replied, “Two digits are correct, but the positions of these two digits are wrong.”
• Peter asked again, “Is the number 8691?”
• John said, “All four digits are correct, but the digits are all in the wrong places.”
What is the number written by John?
Question 3
Given a sequence
3, 3, 1, 9, 4, 3, 3, 1, 9, 4, 3, 3, 1, 9, 4, …
a) What is the 36th number?
b) What is the sum of the first 50 terms?
Self-study input instruction (editorial): use the repeating five-term block shown. Enter both answers separated by a semicolon, in the order a;b.
**Editorial input note:** Use no spaces before or after semicolons.
3, 3, 1, 9, 4, 3, 3, 1, 9, 4, 3, 3, 1, 9, 4, …
a) What is the 36th number?
b) What is the sum of the first 50 terms?
Self-study input instruction (editorial): use the repeating five-term block shown. Enter both answers separated by a semicolon, in the order a;b.
**Editorial input note:** Use no spaces before or after semicolons.
Question 4
Count the number of squares in the given figure.
Question 5
A cockroach is trying to crawl up from a hole. He climbs up 5 steps and then falls down 3 steps and takes a 2 seconds break. If the hole is 14 steps deep, how many breaks does the cockroach take before he climbs all the way up?
Question 6
Find the perimeter of the figure.
Question 7
Ksi counted correctly the number of times the digit ‘2’ appears in the whole number list from 120 to 222. What answer did Ksi get?
Question 8
Arrange the triangles below from the smallest to the largest area.
Question 9
Mr. Joshua runs 6 kilometers everyday from Monday to Friday. He also runs 12 kilometers a day on Saturday and Sunday. How many kilometers does Joshua run in a week?
Question 10
The width of a rectangle is one-third of his length. If the length is 9, what is its perimeter?
Question 11
Three Fridays of a month have the dates which are even numbers. Which day of the week is the 14th of this month?
Question 12
In the following alphametic, all the different letters stand for different digits. Find the two-digit sum SO.
Question 13
Irene has 4 dollars. She wants to buy as many ice creams as possible. Each ice cream costs 50 cents, and 3 ice cream sticks can be exchange for another free ice cream. What is the largest number of ice creams Irene can get? (Two 50 cents are equal to 1 dollar)
Self-study condition (editorial): exchange only sticks Irene currently has; borrowing sticks is not allowed in the graded version.
Self-study condition (editorial): exchange only sticks Irene currently has; borrowing sticks is not allowed in the graded version.
Question 14
There are 8 lamp posts along a stretch of road. In between every 2 lamp posts, there are 2 trees. How many trees are there along that stretch of road?
Self-study interpretation (editorial): count two trees in each gap between neighboring posts on one straight stretch, with no extra trees beyond the end posts.
Self-study interpretation (editorial): count two trees in each gap between neighboring posts on one straight stretch, with no extra trees beyond the end posts.
Question 15
How many triangles are there in the following diagram?
