#100factorial
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davidkbutler.bsky.social
I got to play Home in One Piece at #100factorial today. Damn I love this game. drive.google.com/file/d/1njwv...
Home-in-One-Piece-2017-Making-Your-Own-Sense.pdf
drive.google.com
October 29, 2025 at 4:49 AM
davidkbutler.bsky.social
Tried a new challenge for the Herzberger Quader at #100factorial today.
The Twins: use all the blocks to make two identical shapes.
This is the solution the students came up with today.
Two shapes made of big cardboard cubes. Each is a 3 by 4 rectangle of cubes, with one extra cube at each of the far corners and an extra row of three offset by one at the near edge.
September 10, 2025 at 8:29 AM
davidkbutler.bsky.social
Unfinished Numbers Game from #100factorial yesterday.
A whiteboard with a Numbers Game in process. The instructions say “Help to make as many target numbers as possible, using numbers from the list and any combination of plus, minus, times, divide and brackets. Each calculation can only use each number once, unless the number is in the list more than once.” The list of numbers is 2, 4, 6, 9, 25, 50. The target numbers are the 15 whole numbers from 817 to 831. Most of the target numbers have been crossed out, some of them more than once. The ones not crossed out are 817, 820, 827, 830. Most of the rest of the board is filled with calculations. These are the calculations. (2 × 4 + 9) × 50 - 25 = 825 (2 × 4 + 9) × 50 - 25 + 6 = 831 (2 × 4 + 9) × 50 - 25 - 6 = 819 (6 + 2 + 9) × 50 - 25 + 4 = 829 (6 + 2 + 9) × 50 - 25 - 4 = 821 (6 - 2) × 4 × 50 + 25 = 825 4 × (9 × 25 + 6) - 2 × 50 = 824 4 × (9 × 25 - 6) - 50 = 826 4 × (9 × 25 - 6) - 50 + 2 = 828 50 × (9 × 25 - 9) + 4 × 6 - 2 = 822 4 × (25 - 2) × 9 = 828 50 × 25 - 2 × 4 × 6 × 9 = 818
August 20, 2025 at 10:40 PM
davidkbutler.bsky.social
Hundredfaces from #100factorial yesterday.
Cuisenaire rods arranged into a face. It has a big mouth made of five orange rods, two eyebrows and a nose each made of one orange rods, and two eyes each made of three green rods and one white cube. Cuisenaire rods arranged into a face. The eyebrows and eyes are made of four blue rods. The nose is made of a yellow rod and a purple rod. The mouth is a square made of four orange rods, with teeth around the inside made of 15 white cubes. Cuisenaire rods arranged into a face. Outlining the face are three dark green rods, two orange rods and two blue rods. The eyebrows are yellow rods, the eyes are light green rods, the nose is a purple rod, the mouth is a brown rod and five red rods with six white cubes for teeth. Cuisenaire rods arranged into a face. The hair is made of six yellow rods. The eyebrows are two black rods, with a white cube on one for an eyebrow ring. They eyes are white cubes, with a light green rod and a purple rod for eyeshadow. The nose is two light green rods. The mouth is ten red rods. The ears are two purple rods, each with two white cubes for earrings.
August 20, 2025 at 9:55 PM
davidkbutler.bsky.social
I put this first 90 square puzzle from @mathequalslove.bsky.social on the board at #100factorial yesterday, and students got two different solutions.
A whiteboard with writing on it. The text says "Put an extra digit in some of the squares so that each row and column sums to 90". There is a 3 by 3 square grid drawn in blue with the digits 2, 6, 6 in the top row, and 3, 2, 6 in the middle row, and 6, 3, 2 in the bottom row. Red digits have been drawn next to those digits so that the numbers become 28, 26, 36 in the top row, and 36, 28, 26 in the middle row, and 26, 36, 28 in the bottom row. The rest of the whiteboard has various calculations written on it. A whiteboard with writing on it. The text says "Put an extra digit in some of the squares so that each row and column sums to 90". There is a 3 by 3 square grid drawn in blue with the digits 2, 6, 6 in the top row, and 3, 2, 6 in the middle row, and 6, 3, 2 in the bottom row. Red digits have been drawn next to those digits so that the numbers become 24, 60, 6 in the top row, and 3, 27, 60 in the middle row, and 63, 3, 24 in the bottom row. The rest of the whiteboard has various calculations written on it.
August 20, 2025 at 8:11 PM
davidkbutler.bsky.social
Many people got interested in this puzzle at MASA yesterday. The most fascinating thing is how many people assumed it was a trick question and looked for a solution with sticks inside or outside or on top of each other *assuming that sort of thing was the intent*.
Mostly text with some illustrations. One Hundred Factorial Puzzles, art and games with the Maths Learning Centre www.adelaide.edu.au/mathslearning/play #100factorial Twelve matchsticks Twelve matchsticks can be laid on the table to produce a variety of shapes. For example: Here there is an illustration of three shapes made from matchsticks: a shape like a two by two square with two one-by-one squares attached to it, a three by three square, and a five by one rectangle. Some shapes have the same area and some have a different area. For example, the shapes above have areas 6, 9 and 5. Arrange 12 matchsticks to make a shape with area 4.
July 17, 2025 at 11:37 PM
davidkbutler.bsky.social
Finally, we made the full-depth Well with the Herzberger Quader pieces so that one of the poles supporting the roof went through the hole. #100factorial
A collection of cardboard cubes arranged into a three by three wide and five high box, but with a hole down the middle, which surrounds metal pole supporting the roof of a large open space.
July 16, 2025 at 10:41 AM
davidkbutler.bsky.social
Also at #100factorial today, we confirmed that yes you can make each depth of the Well.
Cardboard cubes arranged into a three by three square with a hole in the middle. Cardboard cubes arranged into three by three wide and two high box with a hole down the middle. Cardboard cubes arranged into three by three wide and three high box with a hole down the middle. Cardboard cubes arranged into three by three wide and four high box with a hole down the middle.
July 16, 2025 at 10:38 AM
davidkbutler.bsky.social
Some creations with the Herzberger Quader blocks at #100factorial today, mostly the work of Alex, a past One Hundred Factorial volunteer who returned for the day.
A collection of cardboard boxes huddled together all standing on their points. There are a few missing cubes in the structure. A collection of cardboard cubes arranged into a ziggurat with a single cube at the top, a three by three layer below that, and a five by five layer below that. A few other cube pieces not used in the construction stand off to the side. A collection of cardboard cubes arranged into a ziggurat with three layers. The top layer is a two by two square. The middle layer has two cubes added to each side of the square. The bottom layer has another two cubes added to the ones added before, plus an extra cube in each corner. The overall effect is very zigzaggy.
July 16, 2025 at 10:34 AM
davidkbutler.bsky.social
Today at #100factorial we played with the Herzberger Quader again. This time we made an empty tower that could fit someone inside.
A tower of cardboard cubes three wide and three long and five high. The photo is taken by someone standing at ground level. Some edges between the cubes are taped together and some aren’t. A tower of cardboard cubes three wide and three long and five high. The photo is taken from above this time. Now it is clear that there is a square hole in the centre of the tower, the inside of which is in dark shadow. A tower of cardboard cubes three wide and three long, with a square hole in the centre. The photo is taken from almost directly above, it’s hard to tell how tall the tower is, except if you look closely you can just count five cubes deep. Also, inside the hole, there is a person standing and you can see their smiling face looking up at you from about one cube down, and their hands waving. The person is me, David Butler.
June 4, 2025 at 8:16 AM
davidkbutler.bsky.social
Can I just say how much joy #100factorial is giving me this year? It is such a pleasure to watch my regular students share mathematical play with each other and with the randoms who pop in just for today. The brightest spot in my week.
May 29, 2025 at 10:00 AM
davidkbutler.bsky.social
More pattern block mirror play at #100factorial yesterday.
A design made of pattern blocks between two angled mirrors. Three sizes of red trapezium are stacked on top of each other with their long sides against the mirror, producing with their reflection a little hexagonal ziggurat. This is reflected two more times. A design made of pattern blocks between two angled mirrors. The design is made of red trapeziums and green triangles stacked on top of each other so that the reflection looks like a wide hexagonal ziggurat. A design made of pattern blocks between two angled mirrors. The design is made of orange squares, pink right-angled triangles, tan narrow diamonds and blue wider diamonds. All of this is is reflected four times around. A design made of pattern blocks between two angled mirrors. The design is made of a base of big blue diamonds, then a layer of dark red trapeziums, then a large number of tan narrow diamonds. This is reflected six times around to make a spectacular design where the tan diamonds look like a bowl and a flower at the same time.
May 28, 2025 at 7:33 PM
davidkbutler.bsky.social
Pattern block mirror play at #100factorial yesterday.
A design made of pattern blocks between two angled mirrors. The design is made of yellow hexagons, little green triangles and a big green triangle, and is reflected six times around. A design made of pattern blocks between two angled mirrors. The design is made of a two grey darts, a blue diamond, a purple concave hexagon, two teal kites, two pink right-angled triangles, two red trapeziums, a yellow hexagon, a little green triangle and two long stripes of tan narrow diamonds along the mirrors’ surfaces. All of this is reflected six times around. A design made of pattern blocks between two angled mirrors. A big red trapezium touches both mirrors, and in the gap behind it is a teal kite and two small green triangles. In front are two bright red small trapeziums, two purple concave hexagons and a big blue diamond. On top is a grey dart and a teal kite. All of this is reflected six times around. A design made of pattern blocks between two angled mirrors. The design is made of a teal kite, two blue diamonds, a purple concave hexagon, and four tan narrow diamonds. All of this is reflected six times around.
May 28, 2025 at 7:25 PM
davidkbutler.bsky.social
Students also worked on the Cars Challenge at #100factorial today.
An A4 page with text and illustrations. The text reads: These eleven blocks are called the HERZBERGER QUADER. CHALLENGE 5: THE CARS. Find collections of some blocks that fit together to make a car one cube wide, then two cubes wide, then three cubes wide, then four cubes wide etc. At the very top, the header says One Hundred Factorial: Puzzles, Art and Games with the Maths Learning Centre. It also has a web address www.adelaide.edu.au/mathslearning/play and a hashtag #100factorial. A shape made of giant cardboard cubes. It has three cubes along the bottom and one cube in the middle on the top. A shape made of giant cardboard cubes. Imagine a shape made from three cubes along the bottom and one cube in the middle on the top, but now imagine it two cubes thick. A shape made of giant cardboard cubes. Imagine a shape made from three cubes along the bottom and one cube in the middle on the top, but now imagine it three cubes thick.
April 2, 2025 at 7:17 AM
davidkbutler.bsky.social
Update! Students got past the six-span bridge at #100factorial today!
Here are bridges that span seven, eight and nine squares. With each one we just stood there looking at them for a while, they were so awesome.
A bridge made of giant cardboard cubes. The gap underneath is seven cubes wide and five cubes high. A bridge made of giant cardboard cubes. The gap underneath is eight cubes wide and four cubes high. A bridge made of giant cardboard cubes. The gap underneath is nine cubes wide and four cubes high.
April 2, 2025 at 4:31 AM
davidkbutler.bsky.social
I have wanted a giant cube puzzle for so long and I can’t believe it’s finally happened. Big thanks to my volunteers Alex and Will, who put in so much effort to construct the cubes. It was just the most glorious thing to behold and my heart is so full. Yay for #100factorial and the Herzberger Quader
March 26, 2025 at 6:46 AM
davidkbutler.bsky.social
We also worked on building bridges with wider and wider gaps below them. These two bridges, each with a gap two cubes wide, look the same but are made of different pieces.
An A4 page with text and illustrations. The text reads: These eleven blocks are called the HERZBERGER QUADER. CHALLENGE 4: THE BRIDGE. Use some blocks to make a bridge that stands on its own, where the blocks meet on whole squares, and that has the widest possible gap underneath. Under this text is an illustration of the eleven blocks, which are all different shapes made by joining two, three or four cubes together. An arrow points to the right to an illustration of a construction of cubes with a gap one cube wide under it, another with a gap two cubes wide, and part of another that looks like it has a gap three cubes wide under it. At the very top, the header says One Hundred Factorial: Puzzles, Art and Games with the Maths Learning Centre. It also has a web address www.adelaide.edu.au/mathslearning/play and a hashtag #100factorial. A bridge made of cardboard cubes, with a gap two wide and two high underneath it. It’s made of a block of three cubes in an L, a block of two cubes and a block of four cubes in an L. A bridge made of cardboard cubes, with a gap two wide and two high underneath it. It’s made of a block of three cubes in an L, a block of two cubes and a block of four cubes in a line.
March 26, 2025 at 6:31 AM
davidkbutler.bsky.social
These students worked hard to put the Herzberger Quader blocks together into a 2 by 4 by 5 box. There was a first failed attempt and then a successful attempt.
An A4 page with text and illustrations. The text reads: These eleven blocks are called the HERZBERGER QUADER. CHALLENGE 1: THE BOX. Fit all of the blocks together to make a 2 by 5 by 4 box. Under this text is an illustration of the eleven blocks, which are all different shapes made by joining two, three or four cubes together. An arrow points to the right to an illustration of a big 2 by 4 by 5 box made of the same cubes. At the very top, the header says One Hundred Factorial: Puzzles, Art and Games with the Maths Learning Centre. It also has a web address www.adelaide.edu.au/mathslearning/play and a hashtag #100factorial. Two students make thumbs-up signs and smile while standing in front of a stack of cardboard cubes that is taller than they are. The stack is two cubes wide and four cubes deep and five cubes wide, except there is a hole in the side where a cube should go, and one extra cube at the very top. Three students manipulate giant blocks made of cardboard cubes stuck together in various shapes. Three students stand in front of a stack of cardboard cubes which is taller than two of the students. The stack is two cubes wide and five cubes deep and four cubes high. Two of the students are giving thumbs-up signs; all three are smiling.
March 26, 2025 at 5:47 AM
davidkbutler.bsky.social
At #100factorial we played with the giant Herzberger Quader pieces.
A collection of eleven blocks made by sticking large cardboard cubes together. Most of them have four cubes, though one has two cubes and two have three cubes. In the background is a pull-up banner saying “One Hundred Factorial: puzzles and games with the Maths Learning Centre”. A collection of eleven blocks made by sticking large cardboard cubes together. Most of them have four cubes, though one has two cubes and two have three cubes. The photo is taken from above so it’s easier to see where one block ends and the next begins.
March 26, 2025 at 5:35 AM
davidkbutler.bsky.social
With huge effort from one of my student volunteers Will, we have now made a set of Herzberger Quader blocks each built from individual 45cm×45cm×45cm cubes.
We’ll be playing with them at the #100factorial session 12-2pm next Wed 26th Mar.

herzberger-quader.de/start
A rectangular stack of cardboard cubes 2 wide and 5 long and 4 high. There is a lot of clear sticky tape joining some of the cubes together. On the wall behind the stack is a diagram of eleven blocks each made by sticking between two and four cubes together. (You can’t see it, but it’s true that those very eleven blocks are what the cardboard cubes are taped together to make, and then they are stacked together into the big 2 by 5 by 4 block.)
March 21, 2025 at 6:10 AM
davidkbutler.bsky.social
Playing Digit Disguises mod 10 at #100factorial today and it’s just awesome.

www.adelaide.edu.au/mathslearnin...
Digit Disguises
www.adelaide.edu.au
March 19, 2025 at 2:36 AM
triangleman.bsky.social
I would be super interested in either (1) what you've learned from playing at #100Factorial, or (2) the learning-center perspective on maths coursework; what does/could/should the relationship between class time and support center work look like?
March 13, 2025 at 5:52 PM
davidkbutler.bsky.social
The Four Fours and its second part had a lot of students involved at #100factorial yesterday.
www.adelaide.edu.au/mathslearnin...
Screenshot of text. The Four Fours, Part 1: The goal is to write whole numbers from 0 to 20 as calculations, each using exactly four of the number 4, and as many of the operations of +,-,×,÷ (and brackets) as you need. For example, 8=4+4-4+4. Six of the whole numbers from 0 to 20 are not possible using these rules. Which numbers are they? Screenshot of text. The Four Fours, Part 2: If you were allowed to also use one other symbol or operation or function as many times as you like (along with +,-,×,÷ and brackets), which one could you choose so that you could write all six of the missing numbers as a calculation using exactly four fours?
March 12, 2025 at 2:22 PM
davidkbutler.bsky.social
A size-5 and a size-7 Sphinx made by student Emma at #100factorial yesterday.
A sphinx shape made out of blue sphinx-shaped tiles on a green background. It’s five times longer than a single tile. Some of the tiles are missing, showing green sphinx-shaped holes. (The sphinx shape can be made out of five equilateral triangles joined zig-zag in a long trapezium, with a sixth triangle at one end of the short edge of that trapezium.) A sphinx shape made out of blue sphinx-shaped tiles on a green background. It’s seven times longer than a single tile. Some of the tiles are missing, showing green sphinx-shaped holes. (The sphinx shape can be made out of five equilateral triangles joined zig-zag in a long trapezium, with a sixth triangle at one end of the short edge of that trapezium.)
March 12, 2025 at 1:41 PM
davidkbutler.bsky.social
And I think I might put out Quarter the Cross at #100factorial today…
March 11, 2025 at 8:58 PM