Distances to Vertices
In the square below, points that are closer to the center than one of the vertices is coloured yellow. The area of the yellow region is 1/2 of the area of the square.
Number Line Mirrors
Starting with some points on a number line, if we put a mirror somewhere on the number line, it will reflect all existing points in itself so that the resulting set of points are symmetrical around it.
Area-Bisecting Lines
Every line going through the center of a square bisects its area. Does every line going through the center of an equilateral triangle bisect its area too?
Circle-Bisecting Lines
All straight lines that bisect the area of a circle go through its center.
Chord-bisecting Chords
A circle of radius 5 has chord AB with length 6. A second chord is drawn here and is bisected by AB.
Friendly Factor Pairs
The number 6 has two pairs of factors: 2x3 and 1x6. These two pairs of factors are called friendly because the sum of one pair is equal to the difference of the other pair, ie. 2+3 = 6-1 = 5.
Sierpinski Pyramid
Let’s remove the central portion of a regular tetrahedron such that what remains are 4 tetrahedrons each with half of the side length of the original.
Digit Sum Divisors
Consider a natural number N and the sum of its digits S. Let’s call a divisor of S a Digit Sum Divisor of N.
Beads in a Bracelet
We have a bracelet made of yellow and green beads, and we want to divide each coloured beads evenly among friends with the least number of cuts.
Finding Paths
In this 4x4 grid, if we choose two squares, for which pairs of squares can we find a path from one square to the other, moving only vertically or horizontally at each step, and visiting every square in the grid exactly once?