AMO 2027 Grades 2-3 SET 8 - Self-study

Ann will be twice Christine’s age in 3 years when Christine will be 40. How many years old is Ann now?

Jeremy’s Math Olympiad class is from 12.45 pm to 3.30 pm. How long is his Math Olympiad class?

Mr. Lee is now 63 years old. He has 3 grandchildren, their ages are 9, 13 and 17. In how many years’ time will Mr. Lee’s age be equal to the sum of his grandchildren’s ages?

The diagram shows some cubes of the same size stacked at a corner of a room. How many cubes are there altogether? (Note: The floor is horizontal and the two walls are vertical. There are no gaps or holes behind the visible cubes.)

A book has 100 pages. How many digits are used to number all pages in the book?

Cans are being stacked on a supermarket shelf. There are 28 cans on the bottom row and 4 cans on the top row. If there are 15 rows and each row is smaller than the one below it by the same number of cans, how many cans are there?

Pi and Ksi were playing touch football against Tom and Fred. Touchdowns were worth 10 points. Pi and Ksi scored 11 touchdowns. Tom and Fred's team scored 13 touchdowns. How many more points did Thomas and Fred have than Pi and Ksi?

Find the missing number in the pattern.

a) 7, 21, 35, …, 63, …

b) 100, 50, 150, 100, 200, …, …

c) 2, …, 18, …, 162, 486.

Self-study input instruction (editorial): use the intended rules of adding 14 in (a), alternating subtract 50 then add 100 in (b), and multiplying by 3 in (c). Enter all six missing numbers in part order, left to right, separated by semicolons. Format: a-first;a-second;b-first;b-second;c-first;c-second.

**Editorial input note:** Use no spaces before or after semicolons.

How many rectangles are there in the figure below?

How many pieces of rope, each 15 metres long, can be cut from a rope 165 metres long? Besides, how many cuts are there needed?

Self-study input instruction (editorial): use ordinary cuts of one straight, unstacked piece at a time. Enter two numbers separated by a semicolon, in the order pieces;cuts.

**Editorial input note:** Use no spaces before or after semicolons.

Marcus cuts a string 8 times so that each resulting string has an equal length of 12 cm. How long is the original string?

If Alice can run around the block 5 times in 20 minutes, how many times can she run around the block in one hour?

The day before two days after the day before tomorrow is Saturday. What day is it today?

Dr. Know-Everything is a chicken farmer. He wants to build a new fence around the chicken enclosure. Each metre of fencing will cost \(\text{\$10}\). Work out the cost of the new fence.

Alice had an activity book with lots of activities, there were 22 pages of mazes. It took Alice 5 minutes to finish a page. How many pages of maze were left after she spent 45 minutes doing the maze?