diff --git a/Misc/Moscow Puzzles/images/101a.png b/Misc/Moscow Puzzles/images/101a.png deleted file mode 100755 index 1c1360d..0000000 Binary files a/Misc/Moscow Puzzles/images/101a.png and /dev/null differ diff --git a/Misc/Moscow Puzzles/images/101b.png b/Misc/Moscow Puzzles/images/101b.png deleted file mode 100755 index e20e913..0000000 Binary files a/Misc/Moscow Puzzles/images/101b.png and /dev/null differ diff --git a/Misc/Moscow Puzzles/images/110.png b/Misc/Moscow Puzzles/images/110.png deleted file mode 100755 index cb511ad..0000000 Binary files a/Misc/Moscow Puzzles/images/110.png and /dev/null differ diff --git a/Misc/Moscow Puzzles/images/120.png b/Misc/Moscow Puzzles/images/120.png deleted file mode 100755 index dd0f70e..0000000 Binary files a/Misc/Moscow Puzzles/images/120.png and /dev/null differ diff --git a/Misc/Moscow Puzzles/images/121.png b/Misc/Moscow Puzzles/images/121.png deleted file mode 100755 index b9bc1d1..0000000 Binary files a/Misc/Moscow Puzzles/images/121.png and /dev/null differ diff --git a/Misc/Moscow Puzzles/images/239.png b/Misc/Moscow Puzzles/images/239.png deleted file mode 100755 index 3e63260..0000000 Binary files a/Misc/Moscow Puzzles/images/239.png and /dev/null differ diff --git a/Misc/Moscow Puzzles/images/252.png b/Misc/Moscow Puzzles/images/252.png deleted file mode 100755 index b34d907..0000000 Binary files a/Misc/Moscow Puzzles/images/252.png and /dev/null differ diff --git a/Misc/Moscow Puzzles/images/255.png b/Misc/Moscow Puzzles/images/255.png deleted file mode 100755 index 7f5343c..0000000 Binary files a/Misc/Moscow Puzzles/images/255.png and /dev/null differ diff --git a/Misc/Moscow Puzzles/images/263.png b/Misc/Moscow Puzzles/images/263.png deleted file mode 100755 index b46f648..0000000 Binary files a/Misc/Moscow Puzzles/images/263.png and /dev/null differ diff --git a/Misc/Moscow Puzzles/main.tex b/Misc/Moscow Puzzles/main.tex deleted file mode 100755 index 6cbd523..0000000 --- a/Misc/Moscow Puzzles/main.tex +++ /dev/null @@ -1,36 +0,0 @@ -% use [nosolutions] flag to hide solutions. -% use [solutions] flag to show solutions. -\documentclass[ - solutions -]{../../../lib/tex/ormc_handout} -\usepackage{../../../lib/tex/macros} - - -\usepackage{subfiles} -\usepackage{graphicx} -\graphicspath{ {./images} } - - -\uptitlel{Intermediate 2} -\uptitler{\smallurl{}} -\title{Warm - Up} -\subtitle{ - Prepared by Mark on \today \\ - \medskip - These problems were originally found in \\ - Boris Kordemsky's \textit{The Moscow Puzzles} -} - -\begin{document} - - \maketitle - - \subfile{problems/217} - \vfill - \pagebreak - - \subfile{problems/101} - \vfill - \pagebreak - -\end{document} \ No newline at end of file diff --git a/Misc/Moscow Puzzles/problems/101.tex b/Misc/Moscow Puzzles/problems/101.tex deleted file mode 100755 index 0cb5db2..0000000 --- a/Misc/Moscow Puzzles/problems/101.tex +++ /dev/null @@ -1,23 +0,0 @@ -\documentclass[../main.tex]{subfiles} - -\begin{document} - - \problem{The Courageous Garrison} - - A courageous garrison was defending a snow fort. The commander arranged his forces as shown in the square frame (the inner square showing the garrison's total strength of 40 boys): 11 boys defending each side of the fort. - - \begin{figure}[h] - \centering - \includegraphics[width=12cm]{101a} - \end{figure} - - The garrison ``lost'' 4 boys during each of the first, second, third, and fourth assaults and 2 during the fifth and last. But after each charge 11 boys defended each side of the snow fort. How? - - \vfill - - \begin{figure}[h] - \centering - \includegraphics[width=4cm]{101b} - \end{figure} - -\end{document} \ No newline at end of file diff --git a/Misc/Moscow Puzzles/problems/110.tex b/Misc/Moscow Puzzles/problems/110.tex deleted file mode 100755 index 954f8df..0000000 --- a/Misc/Moscow Puzzles/problems/110.tex +++ /dev/null @@ -1,16 +0,0 @@ -\documentclass[../main.tex]{subfiles} - -\begin{document} - - \problem{Knight's Move} - - To solve this problem you need not be a chess player. You need only know the way a knight moves on the chessboard: two squares in one direction and one square at right angles to the first direction. The diagram shows 16 black pawns on a board. - - \begin{figure}[h] - \centering - \includegraphics[width=12cm]{110} - \end{figure} - - Can a knight capture all 16 pawns in 16 moves? - -\end{document} \ No newline at end of file diff --git a/Misc/Moscow Puzzles/problems/120.tex b/Misc/Moscow Puzzles/problems/120.tex deleted file mode 100755 index 4757edb..0000000 --- a/Misc/Moscow Puzzles/problems/120.tex +++ /dev/null @@ -1,24 +0,0 @@ -\documentclass[../main.tex]{subfiles} - -\begin{document} - - \problem{One Hundred and Forty-Five Doors} - A prisoner was thrown into a medieval dungeon with 145 doors. Nine, shown by black bars, are locked, but each one will open if before you reach it you pass through exactly 8 open doors. \\ - You don't have to go through every open door but you do have to go through every cell and all 9 locked doors. If you enter a cell or go through a door a second time, the doors clang shut, trapping you. \\ - - \medskip - - The prisoner (in the lower right corner cell) had a drawing of the dungeon. He thought a long time before he set out. He went through all the locked doors and escaped through the last, upper left corner one. What was his route? - - \begin{figure}[h] - \centering - \includegraphics[width=8cm]{120} - \end{figure} - - - \begin{figure}[h] - \centering - \includegraphics[width=8cm]{120} - \end{figure} - -\end{document} \ No newline at end of file diff --git a/Misc/Moscow Puzzles/problems/121.tex b/Misc/Moscow Puzzles/problems/121.tex deleted file mode 100755 index 1cb5f52..0000000 --- a/Misc/Moscow Puzzles/problems/121.tex +++ /dev/null @@ -1,37 +0,0 @@ -\documentclass[../main.tex]{subfiles} - -\begin{document} - - \problem{How Does the Prisoner Escape?} - - This dungeon has $49$ cells. In $7$ cells ($A$ to $G$ in the diagram) there is a locked door (black bar). The keys are in cells $a$ to $g$ respectively. The other doors open only from one side, as shown. \\ - - \medskip - - How does the prisoner in cell $O$ escape? He can pass through any door any number of times and need not unlock the doors in any special order. His aim is to get the key from cell $g$ and use it to escape through cell $G$ - - \vfill - - \begin{figure}[h] - \centering - \includegraphics[width=8cm]{121} - \end{figure} - \vfill - - Extra copies of the dungeon are on the next page. - \pagebreak - - \vfill - \begin{figure}[h] - \centering - \includegraphics[width=8cm]{121} - \end{figure} - \vfill - \begin{figure}[h] - \centering - \includegraphics[width=8cm]{121} - \end{figure} - \vfill - \pagebreak - -\end{document} \ No newline at end of file diff --git a/Misc/Moscow Puzzles/problems/217.tex b/Misc/Moscow Puzzles/problems/217.tex deleted file mode 100755 index 129c04e..0000000 --- a/Misc/Moscow Puzzles/problems/217.tex +++ /dev/null @@ -1,9 +0,0 @@ -\documentclass[../main.tex]{subfiles} - -\begin{document} - - \problem{Mutual Aid} - - During the rebuilding after World War II, the Soviet Union was short of tractors. The machine and tractor stations would lend each other equipment as needed. Three machine and tractor stations were neighbors. The first lent the second and third as many tractors as they each already had. A few months later, the second lent the first and third as many as they each had. Still later, the third lent the first and second as many as they each already had. Each station now had 24 tractors. How many tractors did each station originally have? - -\end{document} \ No newline at end of file diff --git a/Misc/Moscow Puzzles/problems/239.tex b/Misc/Moscow Puzzles/problems/239.tex deleted file mode 100755 index 644a528..0000000 --- a/Misc/Moscow Puzzles/problems/239.tex +++ /dev/null @@ -1,16 +0,0 @@ -\documentclass[../main.tex]{subfiles} - -\begin{document} - - \problem{The Air Parade} - - Volodya asked, ``What plane did you fly during the air parade?'' His father sketched a formation of 9 planes. - - \begin{figure}[h] - \centering - \includegraphics[width=9cm]{239} - \end{figure} - - ``The number of planes to the right of me multiplied by the number of planes to the left of me is 3 less than it would have been if my plane had been 3 places to the right of me.'' How did Volodya solve the problem? - -\end{document} \ No newline at end of file diff --git a/Misc/Moscow Puzzles/problems/252.tex b/Misc/Moscow Puzzles/problems/252.tex deleted file mode 100755 index c920cc8..0000000 --- a/Misc/Moscow Puzzles/problems/252.tex +++ /dev/null @@ -1,40 +0,0 @@ -\documentclass[../main.tex]{subfiles} - -\begin{document} - - \problem{An Elephant and a Mosquito} - - Does the weight of an elephant equal the weight of a mosquito? Let $x$ be the weight of an elephant, and $y$ that of a mosquito. - - \begin{figure}[h] - \centering - \includegraphics[width=10cm]{252} - \end{figure} - - Call the sum of the two weights $2v$, then $x + y = 2v$. - - From this equation we can obtain two more: - - \[ - x - 2v = -y \text{; } x = - y + 2v - \] - - Multiply: - \[ - x^2 - 2vx = y^2 - 2vy - \] - - Add $v^2$: - \[ - x^2 - 2vx + v^2 = y^2 - 2vy + v^2 \text{, or } (x - v)^2 = (y - v)^2 - \] - - Take square roots: - \[ - x - v = y - v \text{; } x = y - \] - - That is, the elephant's weight ($x$) equals the mosquito's weight ($y$). What is wrong here? - - -\end{document} \ No newline at end of file diff --git a/Misc/Moscow Puzzles/problems/255.tex b/Misc/Moscow Puzzles/problems/255.tex deleted file mode 100755 index 775c5f9..0000000 --- a/Misc/Moscow Puzzles/problems/255.tex +++ /dev/null @@ -1,16 +0,0 @@ -\documentclass[../main.tex]{subfiles} - -\begin{document} - - \problem{The Lucas Problem} - - This problem was invented by Edouard Lucas, a French nineteenth-century mathematician. \\ - ``Every day at noon,'' Lucas said, ``a ship leaves Le Havre for New York and another ship leaves New York for Le Havre. The trip lasts 7 days and 7 nights. How many New York-Le Havre ships will the ship leaving Le Havre today meet during its journey to New York? Can you answer graphically? - - \begin{figure}[h] - \centering - \includegraphics[width=10cm]{255} - \end{figure} - - -\end{document} \ No newline at end of file diff --git a/Misc/Moscow Puzzles/problems/263.tex b/Misc/Moscow Puzzles/problems/263.tex deleted file mode 100755 index 624eec5..0000000 --- a/Misc/Moscow Puzzles/problems/263.tex +++ /dev/null @@ -1,16 +0,0 @@ -\documentclass[../main.tex]{subfiles} - -\begin{document} - - \problem{A Shooting Match} - Andryusha, Borya, and Volodya each fired 6 shots, and each got 71 points. - - \begin{figure}[h] - \centering - \includegraphics[width=8cm]{263} - \end{figure} - - Andryusha's first 2 shots got 22 points and Volodya's first shot got only 3 points. \\ - Who hit the bull's-eye? - -\end{document} \ No newline at end of file diff --git a/notes/2023-10-08_19-50.png b/notes/2023-10-08_19-50.png deleted file mode 100755 index 0aea089..0000000 Binary files a/notes/2023-10-08_19-50.png and /dev/null differ diff --git a/notes/2023-10-08_19-52.png b/notes/2023-10-08_19-52.png deleted file mode 100755 index aa44e0a..0000000 Binary files a/notes/2023-10-08_19-52.png and /dev/null differ diff --git a/notes/2023-10-30_11-29.png b/notes/2023-10-30_11-29.png deleted file mode 100755 index dacd108..0000000 Binary files a/notes/2023-10-30_11-29.png and /dev/null differ diff --git a/notes/AACoPtDtbiaLbtaIts.pdf b/notes/AACoPtDtbiaLbtaIts.pdf deleted file mode 100755 index ab466df..0000000 Binary files a/notes/AACoPtDtbiaLbtaIts.pdf and /dev/null differ diff --git a/notes/TODO.md b/notes/TODO.md deleted file mode 100755 index 7978193..0000000 --- a/notes/TODO.md +++ /dev/null @@ -1,49 +0,0 @@ - -# Game ideas - - Math dominos: - - Each problem is a domino tile, by difficulty. - - Score is sum if 1st try, max if 2nd try. Subtract min if no solution. - - Each team can have 2-3 dominos at a time. No free swaps. - - Pick up dominos without knowing problem. - - - что-где-когда: - - All teams solve one problem at once. - - - Spacewar!: - - Two teams, each starts in one root node. - - Graph of problems, symmetric across middle - - easy problems close, hard problems far. - - Goal: capture as many nodes as possible - - Solve a problem, capture a node - - solve a problem on the other team's side, capture their node. - - TODO: a fun way to resolve conflicts? - - -# Topics: -- Divisibility proofs & properties -- 1 exists ==> assume 2 exist -- <= , >= ==> = -- pidgeonhole - -# Handout ideas: -- Notation toolbox -- Propositional logic -- Rubik's group -- Graph combinatorics -- Fourier transforms -- Probabilistic proofs -- Bayesian / Frequentist probability -- Data structures - -# Handouts to clean up: - - Euler's number - - Lattices - - Nim handout - - Stocks - -# Problems to record: - - Nikita: weight of 100 cows - - Seat swapping: everyone wants a seat that's not their own, no two people want the same seat. Each cycle, everyone swaps. Min # of cycles? Solution: 2, reflect. use even and odd cycles. Takeaway: composition of reflections is rotation. - - Geometric optimization: ant on cube shortest path, ant on brick shortest path, ribbon on brick (over-under, h-shape) minimal length, Farthest point from corner of brick - - 180: Sperner lemma and brouwer theorem - - 25 horses. 5 at a time. find top 3? (7 races) diff --git a/notes/handouts/2016-05-22 1194.0.pub (5.22.2016).pdf b/notes/handouts/2016-05-22 1194.0.pub (5.22.2016).pdf deleted file mode 100755 index 88c48b1..0000000 Binary files a/notes/handouts/2016-05-22 1194.0.pub (5.22.2016).pdf and /dev/null differ diff --git a/notes/handouts/Geometric Optima handout.pdf b/notes/handouts/Geometric Optima handout.pdf deleted file mode 100755 index 42b3571..0000000 Binary files a/notes/handouts/Geometric Optima handout.pdf and /dev/null differ diff --git a/notes/handouts/N Sahoo BMC Handout_0.pdf b/notes/handouts/N Sahoo BMC Handout_0.pdf deleted file mode 100755 index 40bf23f..0000000 Binary files a/notes/handouts/N Sahoo BMC Handout_0.pdf and /dev/null differ diff --git a/notes/handouts/com_solutions.pdf b/notes/handouts/com_solutions.pdf deleted file mode 100755 index 35f0f7f..0000000 Binary files a/notes/handouts/com_solutions.pdf and /dev/null differ diff --git a/notes/handouts/nim.pdf b/notes/handouts/nim.pdf deleted file mode 100755 index fa87203..0000000 Binary files a/notes/handouts/nim.pdf and /dev/null differ diff --git a/notes/handouts/notes07.pdf b/notes/handouts/notes07.pdf deleted file mode 100755 index d62cedf..0000000 Binary files a/notes/handouts/notes07.pdf and /dev/null differ diff --git a/notes/handouts/nsa/1.pdf b/notes/handouts/nsa/1.pdf deleted file mode 100755 index 60f5b76..0000000 Binary files a/notes/handouts/nsa/1.pdf and /dev/null differ diff --git a/notes/handouts/nsa/1.sols.pdf b/notes/handouts/nsa/1.sols.pdf deleted file mode 100755 index 3d5df1b..0000000 Binary files a/notes/handouts/nsa/1.sols.pdf and /dev/null differ diff --git a/notes/handouts/nsa/2.pdf b/notes/handouts/nsa/2.pdf deleted file mode 100755 index 87091d1..0000000 Binary files a/notes/handouts/nsa/2.pdf and /dev/null differ diff --git a/notes/handouts/nsa/3.pdf b/notes/handouts/nsa/3.pdf deleted file mode 100755 index 019f165..0000000 Binary files a/notes/handouts/nsa/3.pdf and /dev/null differ diff --git a/notes/handouts/nsa/4.pdf b/notes/handouts/nsa/4.pdf deleted file mode 100755 index 95b6ada..0000000 Binary files a/notes/handouts/nsa/4.pdf and /dev/null differ diff --git a/notes/handouts/nsa/5.pdf b/notes/handouts/nsa/5.pdf deleted file mode 100755 index c7e05f0..0000000 Binary files a/notes/handouts/nsa/5.pdf and /dev/null differ diff --git a/notes/handouts/nsa/6.pdf b/notes/handouts/nsa/6.pdf deleted file mode 100755 index f0e0d35..0000000 Binary files a/notes/handouts/nsa/6.pdf and /dev/null differ diff --git a/notes/handouts/nsa/7.pdf b/notes/handouts/nsa/7.pdf deleted file mode 100755 index c44d804..0000000 Binary files a/notes/handouts/nsa/7.pdf and /dev/null differ diff --git a/notes/handouts/rubik/Group Theory and the Rubik's Cube.pdf b/notes/handouts/rubik/Group Theory and the Rubik's Cube.pdf deleted file mode 100755 index 4da2cf6..0000000 Binary files a/notes/handouts/rubik/Group Theory and the Rubik's Cube.pdf and /dev/null differ diff --git a/notes/handouts/rubik/Rubiks_Cube_Group.pdf b/notes/handouts/rubik/Rubiks_Cube_Group.pdf deleted file mode 100755 index 40db962..0000000 Binary files a/notes/handouts/rubik/Rubiks_Cube_Group.pdf and /dev/null differ diff --git a/notes/handouts/rubik/group.pdf b/notes/handouts/rubik/group.pdf deleted file mode 100755 index 1de008f..0000000 Binary files a/notes/handouts/rubik/group.pdf and /dev/null differ diff --git a/notes/handouts/rubik/rubik.pdf b/notes/handouts/rubik/rubik.pdf deleted file mode 100755 index 757e0c0..0000000 Binary files a/notes/handouts/rubik/rubik.pdf and /dev/null differ diff --git a/notes/handouts/solutions fundamental groups.pdf b/notes/handouts/solutions fundamental groups.pdf deleted file mode 100755 index 7933182..0000000 Binary files a/notes/handouts/solutions fundamental groups.pdf and /dev/null differ diff --git a/notes/handouts/stock.pdf b/notes/handouts/stock.pdf deleted file mode 100755 index d7a6471..0000000 Binary files a/notes/handouts/stock.pdf and /dev/null differ diff --git a/notes/handouts/stocks.pdf b/notes/handouts/stocks.pdf deleted file mode 100755 index 5f10937..0000000 Binary files a/notes/handouts/stocks.pdf and /dev/null differ diff --git a/notes/handouts/tangle.pdf b/notes/handouts/tangle.pdf deleted file mode 100755 index adcc5ac..0000000 Binary files a/notes/handouts/tangle.pdf and /dev/null differ diff --git a/notes/misc/alligators_colored.pdf b/notes/misc/alligators_colored.pdf deleted file mode 100755 index bf10225..0000000 Binary files a/notes/misc/alligators_colored.pdf and /dev/null differ diff --git a/notes/misc/alligators_white.pdf b/notes/misc/alligators_white.pdf deleted file mode 100755 index 45c75c8..0000000 Binary files a/notes/misc/alligators_white.pdf and /dev/null differ diff --git a/notes/misc/croc.html b/notes/misc/croc.html deleted file mode 100755 index 387da2a..0000000 --- a/notes/misc/croc.html +++ /dev/null @@ -1,138 +0,0 @@ - -Alligator Eggs! - - - -

Alligator Eggs!

-

A puzzle game by Bret Victor / May 1, 2007

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-

Materials

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Step 1: Print out this PDF onto six or so - different - colored - sheets - of - paper.
-(Even better, photocopy it onto cardstock.)

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Step 2: Print out this PDF onto a couple white sheets of paper.

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Step 3: Cut out the pieces!

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Pieces

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These are hungry alligators:

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Hungry alligators are hungry. They'll eat anything that's in front of them! But they are also responsible alligators, so they guard their families.

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These are old alligators:

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Old alligators are not hungry. They've eaten enough. All they do is guard their families.

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These are eggs:

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Eggs hatch into new families of alligators!

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Families

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Here's a small family:

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A green alligator is guarding her green egg.

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Here's a slightly bigger family:

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A green alligator and red alligator are guarding a green egg and a red egg. Or, you could say that the green alligator is guarding the red alligator, and the red alligator is guarding the eggs.

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Here's a huge family!

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We've got yellow, green, red alligators guarding this family. They are guarding three things: a green egg, an old alligator, and a red egg. The old alligator is guarding a yellow egg and a green egg.

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Notice that eggs only use the colors of the alligators guarding them. You can't have a blue egg without there being a blue alligator around to guard it.

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Eating

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Now, things are going to get messy. Here are two families, side-by-side:

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That green alligator sure is hungry. And there's a yellow family, right in front of her mouth, and it looks tasty!

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I think you know what happens next.

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Unfortunately, the green alligator's eyes were bigger than her stomach. She ate too much!

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And so she dies, and goes off to alligator heaven. But, the story doesn't end there. Because the green alligator died, the green egg starts to hatch...

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Amazingly, it hatches into exactly what the green alligator ate. It's the miracle of life!

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Now, we're down to one family. We have a red alligator guarding a yellow alligator and a red egg, and the yellow alligator is guarding her yellow egg.

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But that yellow alligator sure is hungry, and there's a tasty red egg in front of her. Here we go again...

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Poor alligator. Even a single egg is too much for her stomach!

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The yellow alligator dies... but once again, the yellow egg starts to hatch...

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And it hatches into exactly what the yellow alligator ate!

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Now, there's nothing for anyone to eat, so we stop.

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The Eating Rule

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That was an example of the first rule of the game: the eating rule.

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The eating rule says that if there are some families side-by-side...

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the top-left alligator eats the family to her right.

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Then, that alligator dies. But if she was guarding any eggs of the same color, each of those eggs hatches into what she ate.

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The Color Rule

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Continuing with the example above, the orange alligator eats the yellow family, leaving this:

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Now, the green alligator at the top-left wants to eat the family to her right. But before she can do so, we need to look at the color rule.

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The color rule says that if an alligator is about to eat a family, and there's a color that appears in both families, we need to change that color in one family to something else.

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In the picture above, green and red appear in both the first and second families. So, in the second family, we switch all of the greens to cyan, and all of the reds to blue.

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Now that they don't share any colors, we can eat!

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And eat!

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And eat!

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And eat, until there's nothing more that can be eaten.

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Old Alligators

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There's only one more rule in this game, and it has to do with old alligators:

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The top-left alligator here is not hungry. She's not going to eat anything. All she cares about is her family. So, how does she die?

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She dies when she's only guarding one thing. Right now, she's guarding both a green family and a red family. They need her to take care of them. But that green alligator is hungry. The green alligator eats the red family...

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Now, the old alligator is only guarding a single family. That family can take care of itself. She's no longer needed. So, she grows old and dies.

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That is the old age rule. When an old alligator is just guarding a single thing, it dies.

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Now, the red alligator eats the yellow family, and there's no more that can be eaten.

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Gameplay

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The game would consist of a series of puzzles, challenging the player to devise a family that, when fed X, produces Y. For example:

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Here are two families. They are named "True" and "False":

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And here is a family called "Not":

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When "Not" eats "True", it produces "False". And when "Not" eats "False", it produces "True". What colors should the two eggs at the bottom be?

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(For this to work well, we'd need a better color rule, to explain that families with different colors in the same "pattern" are equivalent.)

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These puzzles could be embedded into a story. The player would have to solve each puzzle to see what happens next. Alternatively, this could be made into a board game. Each player would roll a die, travel forward a number of spaces, and solve the puzzle at the destination.

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Theory

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This game represents the untyped lambda calculus. A hungry alligator is a lambda abstraction, an old alligator is parentheses, and eggs are variables. The eating rule corresponds to beta-reduction. The color rule corresponds to (over-cautious) alpha-conversion. The old age rule says that if a pair of parentheses contains a single term, the parentheses can be removed.

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Variations

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Oliver Steele pointed out that family roles are very important to children, and more could be made of the concept of grandparent alligators, parents, babies (eggs), and so on. Currently, variable names are represented with colors. Both are arbitrary, and require renaming/recoloring rules to avoid capture. An alternative may be something like de Bruijn indices, corresponding to birth order and family relation.

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Oliver also suggested that kids might not like the idea of parents dying, and perhaps alligator removal could be explained as moving away.

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By changing the game so alligators are greedy, and eat everything to their right, we represent a right-associative lambda calculus. This seems to eliminate a lot of old alligators (parentheses) in Church numerals, the Y combinator, etc. Unfortunately, it means that old alligators have to be born when an alligator eats more than one thing, among other problems. I'd still like to figure out how to make Church numerals (repeated application) look less ugly.

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Schematic Form

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I've found that a schematic form of alligator calculus is actually rather handy for calculating lambda terms by hand. We draw a lambda as a line with a mouth. Parentheses are a line without a mouth. Here's the identity function:

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Here are some Church numerals:

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Here are boolean AND and OR (assuming the standard definitions for TRUE and FALSE):

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The Y combinator:

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I don't know if these are any easier to read than the standard notation, but I've found them to be easier to work with, using pencil and paper. I imagine the terms eating one another and hatching below. I don't get lost in a long chain of symbols, losing track of what's applying to what.

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