AMO 2019 Primary 3 (Grade 3)

Find the value of $100-80+60-40+20-10+8-6+4-2$.

How many three-digit numbers have a digit sum of 5? The hundreds digit cannot be 0.

I am thinking of a number. Subtract 17 from it and then multiply by 7 to get 91. What is half of my number?

Here is a method for squaring a number ending in 5. For $25\times25=625$, calculate $2\times(2+1)=6$ and append 25. Similarly, $35\times35=1225$ uses $3\times4=12$, and $45\times45=2025$ uses $4\times5=20$. These squares always end in 25. Find the sum of the digits of $455\times455$.

Isabella has stacked unit cubes in a corner as shown. If she continues the pattern until the stack is six cubes high instead of four, how many more cubes does she need?

In the repeating pattern $\mathrm{MOEMSMOEMSMOEMS}\ldots$, how many letters M occur in the first 38 letters?

The five-digit number $\overline{A6A6A}$ is divisible by 11. What digit is $A$?

Ava’s PIN is a four-digit number whose digits sum to 22. From left to right, the first two digits are equal. The second digit is twice the third, and the first is four times the fourth. What are the first three digits of her PIN? For example, if the PIN were 1542, answer 154.

Emma fills the shown $3\times3$ grid with the numbers 1 through 9, one in each box. Every row, column and diagonal must have the same sum. Some numbers are already placed. What number must go in the box marked $X$?

If the entire outside of the solid shown is painted black, how many unit square faces are painted?

A MOEMS-tile is shaped like the letter M as shown: a $5\times5$ square with two $4\times1$ rectangles removed. Jimmy places as many such tiles as possible on a $6\times12$ board without overlap. What is the maximum number of tiles he can place?

Adam and Brady each start a game with 10 points. In every round, the winner gains 3 points and the loser loses 3 points. Adam wins exactly four rounds, and Brady finishes with 28 points. How many rounds did they play altogether?

A group planned a trip using 10 buses, with the same number of people on each bus. They cancelled 3 buses and redistributed everyone equally among the remaining buses. Each remaining bus then had 3 more people than originally planned. How many people were going on the trip?

The place cards shown are folded along the dotted line so that only a number or a letter is visible. Chrissy sees all five cards, some showing numbers and some showing letters. The visible numbers sum to 9. How many different sets of visible numbers are possible?

In the cryptarithm shown, different letters represent different digits, and repeated letters represent the same digit. Given $A=5$ and $O=4$, what is the greatest possible value of $\overline{WIN}$?