AMO 2018 — Primary 6 (Grade 6)

Find the following sum $150 + 195 + 255 + 210 + 120$.

How many whole numbers between 41 and 50 (inclusive) are multiples of either 2 or 3 or 5?

The numbers 123456789 and 987654321 are added. This sum is divided by a single digit number, leaving no remainder. How many possible single-digit numbers could have been used?

The points A, B, C, D and E are arranged as shown at the right so that no three points lie on a straight line. How many different triangles can be formed, connecting three of these points at a time to use as vertices?

Faye and Ingrid are fruit vendors. Faye’s total fruits is 21 more than $1rac{1}{2}$ of Ingrid’s total fruits. Their total number of fruits is 216. How many fruits does Faye have?

Michael opens his favorite mathematics puzzle book and notes that the product of the page numbers facing him is 462. Find the sum of these two page numbers.

In the repeating pattern below, how many letter O’s will be written before the 1808th letter?

ODAKOOODAKOOODAK...(and so on)

Consider the figures below. How many dots will the 22nd figure contain?

Jericho has a collection of stickers. When the stickers are arranged in piles of 6, there are 5 stickers left over. When the stickers are arranged in piles of 22, there are 21 stickers left over. When the stickers are arranged in piles of 14, there are 13 stickers left over. What is the least number of stickers Jericho can have in his collection?

The first 73 odd whole numbers are written. How many times does ‘3’ appear as a digit?

Find the sum of the digits of the sum: $1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 + 2048$.

Samantha looked at a clock and realized that the number of hours remaining until noon was $3/5$ of the number of hours that had passed since midnight. What time did the clock show? (Disregard the colon in your answer. Example, if your answer is 3:00, write 300)

Given □ + △ + ◇ = 60, △ + ◇ + ☆ = 44, ◇ + ☆ + □ = 52, and △ + ◇ + ☆ + □ = 74, find the value of ☆ + □ + △.

Remi had a square garden that had an area of 16 square meters. She extends the length of the garden by 2 meters and the width by 3 meters. What is the new perimeter, in meters, of the garden?

Three sisters have the same birthday, but were born in different years. Five years ago, the oldest sister’s age was 9 times the age of the youngest sister. At that time, the age of the middle sister was 4 times the age of the youngest sister. Today, the oldest sister's age is four times the age of the youngest sister. Today, how old is the oldest sister?

The figure shown is created by overlapping three 2 cm-by-6 cm rectangles. Suppose an ant moves around the perimeter traveling at 1 cm/second on each horizontal segment and 2 cm/second on each vertical segment. How long, in seconds, did the ant take to complete its entire journey?

Consider four right angled triangles with leg lengths 1 cm × 4 cm, 2 cm × 4 cm, 3 cm × 4 cm, and 4 cm × 4 cm. Arrange the four triangles, without overlap. What is the smallest possible area, in square cm, of the rectangle that can fit them? (Legs of a right-angled triangle are the sides beside the right angle)

Ananya wants to tile a floor that is 24 m by 40 m. There are two types of tiles: a square that is 2 m on a side and an L-shape as shown. The L-shaped tile can be turned over or rotated if needed. What is the least number of tiles Ananya needs to tile the floor completely?

In a family, there are four children. Angela’s age is the sum of Betty’s and Carla's ages. Four years ago, Daniel's age was the sum of Betty’s age then and Carla’s age then. Eight years ago, Angela’s age was twice Daniel's age then. Betty and Carla are twins. How old (in years) is Betty?

In the following cryptarithm, each different letter represents a different digit. Assuming a number cannot start with 0, find the last three digits of the smallest possible sum. (Example, if your answer is 1234, then write 234.)

```text
MINED
+DENIM
```