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?
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?
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).
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.
Nonlinear Dots
Here’s a way to put 6 dots into a 3x3 grid such that no 3 dots form a straight line.
Combination Lock
There’s a combination lock with a 3 digit code with no repeated digits, and for each of our attempts to guess the code it tells us the number of correct digits and ones in the correct places.