AMO 2018 Grade 3

What is the value of the following?

$72 + 60 + 48 + 36 + 24 + 12$

Terry and Gerald were in an essay writing competition. Gerald wrote 57 more words than Terry. They wrote 777 words altogether. How many words did Gerald write?

Heinz has 87 chocolates and receives 4 chocolates every week. Jed has 137 chocolates and gives away 6 chocolates per week. After how many weeks will they have the same number of chocolates?

There are three numbers each represented by one of the symbols □, △, and ◇. Given that the following statements are true, what number does the sum ◇ + □ represent?

Lois is making rows of dots. The first five rows of dots are shown. Each additional row has one more dot than the row above it. How many total dots are there in the first 16 rows combined?

Gina’s playroom is shown below (each small square is 1 meter long). Suppose her parents extend the length of the playroom by 6 meters and the width by 9 meters. What will be the new perimeter, in meters, of the playroom?

Find the value of

$31 + 42 + 53 + 64 + 75 + 86 + 97$.

Helen wrote the first 25 even numbers. How many times did Helen write the digit “3”?

Ryan has a collection of baseball cards. If the cards are arranged in piles of four, three cards will be left. If he arranges them in piles of seven, three will be left. Suppose the cards are arranged in piles of 28. How many cards will be left?

Marci looked at a clock and realized that the number of hours that had passed since midnight was twice the number of hours remaining until noon. What time did the clock show?

(Disregard the colon in your answer. Example, if your answer is 3:00, write 300)

Each of the whole numbers 1 through 8 is written on 8 cards, one number on per card. Four cards are given to each of two players. The sum of Player One’s cards is 23. What is the highest single card could Player Two possibly have?

In the following cryptarithm, each different letter represents a different non-zero digit. What is the smallest possible value for the difference?

In the repeating pattern below, how many letter O’s will be written before the 1234th letter?

ODAKOOODAKOOODAK...(and so on)

Grandpa said, “If you divide my age by 4 and then add 32 years, the result is 22 years less than my age.” How old is Grandpa, in years?

The numbers 1 through 9 are placed in the diagram, one in each circle. The sum of the numbers along each line is 21. What is the sum of the numbers in the shaded circles?