Let `{x}` denote the fractional (non-integer) part of `x`. As examples: `{3} = 0`, `{0.5} = 0.5` and `{4.13} = 0.13`. If `{n} + {2n} = 1.2`, how many values can `{n}` take?
Two candles have different lengths and thicknesses. The shorter candle lasts for 11 hours, while the longer one lasts for 7 hours.
Both candles are lit at the same time and it is given that the candles melt uniformly in length. After 3 hours, they have the same lengths.
Find the ratio of the longer candle to the shorter candle.
You are planning a 5-day WMC training camp. Each day, the team either practises running (for the Lightning round), doing mathematical problem solving, or engaging in recreational activities.
Because of fatigue, the team cannot have two consecutive days of running. In addition, to prevent complacence, the team cannot have two consecutive days of recreation. It's not necessary for all three activities to be covered, so for example a camp schedule could involve only running and recreation, and no maths.
Find the number of ways this training camp can be planned.
Find the radius, `r`, of a sphere, such that the numerical value for the volume of the sphere equals the numerical value for the surface area of the sphere.
Assume the same base units are used.
Let p be a prime larger than 7. What is the remainder when `p!` is divided by `p+1`?
A solid metal sphere with radius `6cm` is melted and put into a mould for a solid metal cone with height `2cm`.
If all the metal is used to make the cone, what is the radius of the cone's base?
Giles has n candies. When he splits them amongst a group of 2 people, the candies are evenly distributed.
If the group consists of 3 or 5 people, there are two candies left over. If the group consists of 7 people, there are 5 candies left over.
What is the smallest possible value of n?
Find the area, in `cm^2`, of a triangle with sides `9cm`, `40cm` and `41cm`.
If `x = y^3` and `y =` 3`sqrt(z^(-1/3))`, express `x` in the form `x = z^n` and give the value of `n`.
In Pascal's Triangle, the 2nd row is made up of the numbers 1, 2, 1.
Find the difference between the 10th number in the 11th row and the 11th number in the 10th row.
Find the integer value of `m`, so that the following inequality is true for all `x`:
`x^2 + 2(m-1)x + 4m - 7>0`
Four schools are competing in a cross-country race. School A has 3 runners, School B has 2 runners, School C has 4 runners, and School D has 1 runner.
For scoring purposes, the finishing order of the race only considers the school of each runner. How many different finishing orders are there for the 10 runners?
The sum of the digits in 2017 is 10.
How many numbers from 2000 to 3000 also have this property? (including 2017)
The graph of a parabola has an `x`-intercept of `(-2, 0)`, passes through `(1, 42)` and has its axis of symmetry at `x = 3`.
Express the parabola in the form `y = a*(x-p)*(x-q)` to find the value of `a + p + q`.
The operation ⊙ is defined as follows: a ⊙ b = `3a^2 + 2b`.
Determine the value of k, such that 11 ⊙ k = 2017.
The area of a square is `72 cm^2`. Find the exact length of its diagonal.
A hotel has rooms that can accomodate up to two people. Couples can share a room, but otherwise men will only share with men, and women will only share with women.
How many rooms are needed to guarantee that any group of 100 people can be accommodated?
Calculate the value of `2023^2 - (2021xx2025)`.
Find the sum of the first 99 positive integers that are divisible by 7.
The number formed by the string of digits: 22756ab is divisible by 55, where a and b are digits.
Find the sum of all possible values of the string ab.
(If a was 1 and b was 7, the string ab would be 17).
It takes twelve painters five hours to paint a house. Assuming that all the painters work at the same pace, how long would it take, in hours, for eight painters to paint two identical houses.
How many positive five digit integers less than 50,000 contain the digits '123' consecutively and in that order?
A thief stole `9/16` of Mr. Lee's money and spent `9/16` of the money stolen. The thief was then caught, and the remaining money was returned to Mr. Lee.
The remaining money was 588 dollars less than the amount Mr. Lee had after being robbed. How many dollars did Mr. Lee have before the theft?
The value of `45^2` is also the concatenation of two numbers whose sum is `45`. What are those two numbers?
HINT: The concatenation of `9` and `17` is `917`. The concatenation of `17` and `9` is `179`.
The attached diagram shows two equilateral triangles. What is the value of x, in degrees?
k,w and p are integers such that `[((x^2*y^(-6)*z^3)^(-2)) / ((x^(-5)*y^(3)*z^2)^(-1))]^-2 = x^k*y^w*z^p`
What is the value of k + w + p?
Find the number of diagonals in the interior of a convex 9-sided polygon.
What is the last digit of `9^(9^9)` ?
How many five-digit numbers can be created from the digits 1, 2, 3, 4 and 5? (no repeats)
A circle has a chord of length 8cm. The shortest distance between the centre of the circle and the given chord is 3cm. Find the radius of the circle, in cm.
