| TOURNAMENT | DATE | DURATION(mins) | LEVEL |
| 2023 PI Day Tournament | 03/14/2023 | 60 | Grade 3 |
Problem 1
Compute \((2 + 3 \times 3 - 1) \times 5 - 4 \div 2.\)
Problem 2
Triple a number, and subtract \(2\), the result is \(10\). What is the original number?
Problem 3
Alex has got \(9\) apples and \(2\) bananas. He gives \(3\) apples to his friend Ben, who gives him bananas in return. Afterwards Alex has got the same amounts of apples as bananas. How many bananas did Alex get from Ben?
Problem 4
Evaluate \(19 - 18 + 17 − 16 + 15 − 14 + · · · + 3 − 2 + 1.\)
Problem 5
What is the sum of the two numbers that are twice as far from 70 as from 40?
Problem 6
How many whole numbers lie in the interval \(\frac{5}{3}\) and \(\pi\)?
Problem 7
Jan gives away 10 muffins out of every 12 that she bakes. If Jan bakes 60 muffins, how many does she give away?
Problem 8
A class has twice as many boys as girls. If there are 30 students in the class, how many of them are girls?
Problem 9
A cake weighs \(900\) g. Paul cuts it into \(7\) pieces. The biggest piece weights exactly as much as the other six pieces combined together. How much does the biggest piece weigh in g.
Problem 10
Lisa has several dogs. Her dogs have 18 more legs than noses. How many dogs does Lisa have? (All dogs have 4 legs).
Problem 11
\(99\) runners start in a running race. At the finish, there are \(30\) more runners behind Thomas than there are in front of him. In which position did Thomas finish?
Problem 12
If the three digits of a three-digit number are multiplied you get \(105\). Which result do you get, by adding the three digits?
Problem 13
We subtracted the smallest three-digit number with all different digits from the greatest three-digit number with all different digits. What is the result?
Problem 14
Grandma gives \(100\) marbles to her ten grandchildren. No two children get the same amount of marbles and each child gets at least one marble. Anna gets the most. What is the maximum number of marbles that Anna could get?
Problem 15
The numbers \(1, 2, 3, 4\) and \(5\) are written into the squares on the following figure. The sum of the three numbers in the horizontal row, should be the same as the sum of the three numbers in the vertical column. How many different numbers can be written in the center square?
Problem 16
A gum-ball machine contains 9 red, 7 white, and 8 blue gum-balls. What is the least number of gum-balls a person must buy to be sure of getting four gum-balls of the same color?
Problem 17
In a magic garden there are magic trees. On each tree there are either \(9\) pears and \(3\) apples or \(12\) pears and \(4\) apples. In total there are \(30\) apples on the magic trees. How many pears in total are hanging on the magic trees altogether?
Problem 18
Arrange the digits \(1, 3, 9, 0\) and \(6\) to form the biggest 5-digit number that is divisible by 4. What is this 5-digit number?
Problem 19
On main street, there are 11 houses in a row. Each house has at least one inhabitant. Each pair of neighbouring houses have at most 5 inhabitants. What is the maximum number of inhabitants living on main street?
Problem 20
How many different three-digit integers we can make by using digits from the set \(\{1,1, 2, 2, 2, 3\}\), where each digit can be used multiple times but no more than the number of appearance in the set. For example, 1 can be used up to two times, but not three times.