Nonlinear Arrangements
Here’s an arrangement of the numbers 1 to 4, and what it looks like plotted into a 4x4 grid such that each row corresponds to a number in the arrangement. Notice that the 3 dots on the bottom right form a straight line.
Probability Thoughts
If the possible fairness of a coin is a continuum, the probability of the coin being exactly fair (50H/50T) is 0. To begin exploring, let’s say the coin can only be rigged heads (100H/0T), fair (50H/50T), or rigged tails (0H/100T).
Crossing Numbers
From the list of numbers 1 to n, cross out every other number starting with the smallest and repeat the process with the remaining numbers until only one number is left. What number would that be for a given n?
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?
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.
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.
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.
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.
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.
Circle-Bisecting Lines
All straight lines that bisect the area of a circle go through its center.