100! Factorial Puzzles

David Butler (@DavidKButlerUoA) of the Maths Learning Centre at the University of Adelaide runs a puzzle and games club called “One Hundred Factorial” (named after the first puzzle the club tackled – read more here).

Across the years, many of these puzzles have been shared through photos on Twitter using #100factorial. Here I aim to curate a list of all the puzzles that have been shared, with descriptions and possible solutions, eventually with some degree of organisation, to aid in finding puzzles quickly in the future.

Only Ones
Using any or all of the operations of addition, subtraction, multiplication, division and exponentiation (and brackets), and as many of
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One Spot Dice
You have two blank 6-sided dice. You are allowed to choose any number of the twelve faces and draw exactly
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Number of Letters
The numbers seven, eleven, fifteen, nineteen make a sequence where the numbers go up by 4 each time. But if
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Lousy Labelling
Three boxes filled with lots of balls are on the table. One box is full of red balls, one is
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Combo Cube
Eight cubes are marked with one dot on two opposite faces, two dots on two opposite faces and three dots
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Convexity of Deltahedra
Claim: There is a convex deltahedron with every even number of faces from 4 to 20, except one. Investigating non-convex
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Dividing Dice
A standard six-sided die spontaneously starts to divide like a living cell. The spots on the die move during the
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Broken Calculator
Imagine your calculator is broken. Although it will still display numbers, only the 4 key, + key, = key, and
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Four Dots, Two Distances
Find all configurations of four (distinct) points in the place that will determine exactly two distinct (non-zero) distances.
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Jiggly Numbers
A positive integer is said to be jiggly if it has four digits, all non-zero, and no matter how you
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