Algebra
Number Theory
Combinatorics
Geometry
Logic
100
Bob bought a pie. While he was at work, his sister ate 1/3 of the pie, his friend at 1/5 of the remainder, his mom ate 4/9 of the remainder and his dad at 1/4 of the remainder. What fraction of the pie does Bob find when he gets back from work?
2/9
100
What is 1001101011 in decimal?
619
100
Mary typed a six-digit number, but the two 
s she typed didn't show. What appeared was 
How many different six-digit numbers could she have typed?
100
A regular polygon has 11 sides. How many diagonals does it have? A diagonal is a line segment that joins two corners but is not a side. One diagonal is shown in the picture.
44
100
I'm an integer. If you double me up and subtract 67 from me, I become the same number. What am I?
67
200
169 students take physics and/or chemistry: 149 take physics and 119 take chemistry. How many students take both physics and chemistry?
99
200
Charles was born in a year between 1300 and 1400. Louis was born in a year between 1400 and 1500. Each was born on 6 April in a year that was a perfect square. Each lived for 110 years. In what year while they were both alive were their ages both perfect squares on 7 April?
1469
200
How many integers from 10 to 1000 have strictly decreasing digits? (ex 941 and 70 are ok but 769 and 66 are not)
165
200
An obtuse iscoscele triangles has a base of 8 and two legs of 5. What is the height?
3
200
A box contains 28 red balls, 20 green balls, 19 yellow balls, 13 blue balls, 11 white balls, and 9 black balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 15 balls of a single color will be drawn?
76
300
A train usually takes 13 hours to get from A to B. If the train's speed is 5km/h less than usual, the trip takes an hour longer. What is the distance from A to B?
910 km
300
There are a number of eggs in a box. If we take 3 eggs each time, 1 is left in the end; if 5 are taken each time, 2 are left in the end; if we take 7 each time, 3 are left in the end. How many eggs are in the box at least?
52
300
On any standard die, the sum of the numbers on opposite faces is equal to 7. If two standard dice are tossed, what is the probability that the sum of the numbers on the 10 visible faces is equal to 31? Express your answer as a common fraction.
1/18
300
Two congruent circles centered at points A and B each pass through each other’s center. The line containing both A and B is extended to intersect the circles at points C and D. THe circles intersect at two points, one of which is E. What is the measure of angle CED?
120
300
Lion always lies on Mondays, Tuesdays, and Wednesdays.
Lion always tells the truth on other days.
Unicorn always lies on Thursdays, Fridays, and Saturdays, and always tells the truth on other days.
On Sunday, everyone tells the truth.
Lion says: “Yesterday was one of my lying days."
Unicorn says: “Yesterday was one of my lying days, too.”
What day is it?
Thursday
400
A swimming pool that can contain a maximum of 162 cubic meters of water is filled up by three taps. Unfortunately, the operator forgot to shut off the drain pipe, which drains the full pool in 18 hours. As a result, it took 36 hours to fill the pool. How much water (in cubic metres) was wasted down the drain pipe while the pool was being filled?
324 cubic metres
400
Mary chose an even four-digit number n. She wrote down all the divisors of n in increasing order from left to right: 1, 2, …, n/2, n. At some point, Mary wrote 323 as a divisor of n. What is the smallest possible value of the divisor written to the right of 323?
340
400
Alicia has 6 pairs of shoes, identical except for colour: 3 of the pairs (6 shoes) are brown, 2 pairs are red, and 1 pair is green. Alicia is completely colour blind, so she picks a left shoe and a right shoe at random. What is the probability that the two shoes are of the same colour? Express your answer as a common fraction.
7/18
400
A 1X2 rectangle is inscribed in a semicircle with longer sides on the diameter. What is the area of the semicircle?
π (pi)
400
Kiran has a box containing three different types of fruit: apples, pears, and bananas. In the box, 21 pieces of fruit are not apples, 25 pieces of fruit are not pears, and 28 pieces of fruit are not bananas. How many pieces of fruit are in the box?
37
500
The table below displays some of the results of last summer's Frostbite Falls Fishing Festival, showing how many contestants caught n fish for various values of n:
n 0 1 2 3 ... 13 14 15
Number of Contestants 9 5 7 23... 5 2 1
who caught n fish
In the newspaper story covering the event, it was reported that
(a) the winner caught 15 fish
(b) those who caught 3 or more fish averaged 6 fish each
(c) those who caught 12 or fewer fish averaged 5 fish each
What was the total number of fish caught during the festival?
943 fish
500
How many four-digit integers abcd, with 
, have the property that the three two-digit integers ab<bc<cd form an increasing arithmetic sequence? One such number is 4692, where a=4, b=6, c=9 and d=2.
17
500
Tina randomly selects two distinct numbers between 1 and 5 (inclusive), and Sergio randomly selects a number between 1 and 10 (inclusive). What is the probability that Sergio's number is larger than the sum of the two numbers chosen by Tina?
2/5
500
Right triangle ABC has leg lengths AB = 20 and BC = 21. Including AB and BC, how many line segments with integer length can be drawn from vertex B to a point on hypotenuse ?
13
500
A town has 2017 houses. Of these 2017 houses, 1820 have a dog, 1651 have a cat, and 1182 have a turtle. If x is the largest possible number of houses that have a dog, a cat, and a turtle, and y is the smallest possible number of houses that have a dog, a cat, and a turtle, then what is x - y?
563