TechnicalImpulse

My problem with the 2-dimensional political graph is that it's always drawn with orthogonal axes, suggesting that the two attributes are independent and the quadrants are equally populated. Which is simply not the case.

"linear algebra which is also graph theory" => tell me that your matrices are sparse without using the word "sparse"

Not to be That Grumpy Guy, but I stand with Bill Gosper (en.wikipedia.org/wiki/Bill_Go...) in thinking that the decimal digits of pi are too number-base-centric and we ought to be doing something around the continued fraction instead.

So there are 63 Bedlam siblings. They all have different numbers of solutions. The original puzzle has 19186 solutions. Its siblings range from 16457 to 30613 solutions.
2/2
#puzzles #combinatorics #block-packing

The Bedlam Cube has 7 chiral pieces. (Chiral = no plane of mirror symmetry.) Reflecting the whole set would, of course, have the same set of solutions (mirrored). But reflecting only some of them results in a whole new puzzle.
1/2
#puzzles #combinatorics #block-packing

#puzzles

This is one solution to the Bedlam Cube, a polycube block-packing puzzle. Searching for new block-packing puzzles (and not Sudoku) is why I've been playing with an Exact Cover solver.

It's well known that Sudoku can be written as an Exact Cover problem. But upon browsing Sudoku's lesser-known siblings here: www.nikoli.co.jp/en/puzzles/ it strikes me that many (most?, all?) are also equivalent to Exact Cover. Anyone done a comprehensive study?
#puzzles #sudoku #combinatorics

I'd call that a "parity" argument and yes, I looked for one of those too. (Not only mod 2 - the checkerboard - but also mod 3 and mod 4 can be useful sometimes.)

The space remaining is an 'L', which we've already used.
Q.E.D?

Now consider cells (2,1) (1,1) and (1,2) that wrap around the top left of the 'X', and also the similar ones that wrap around the bottom left (4,1) (5,1) and (5,2). There's only two pieces that can do that: 'U' and 'L'. Again without loss of generality, put one above, and one below.
2/3

Well, there are various degrees of "exhaustion". Start with: there's only 1 place (modulo symmetry) to place the 'X' without isolating a region with fewer than 5 cells. Without loss of generality, let's place it vertically centered touching the left edge. X: (3,1) (2,2) (3,2) (4,2) (3,3).
1/3

What are the rules of the game? If you are allowed to use the same piece more than once, you can tile the 5x4 with 2 'U's, an 'X', and an 'I'.

#woodturning #woodworking

It's a bowl. It's a cutting board. It's half-way in between.
For cutting dry ingredients (think nuts or chocolate) that have a tendency to spray little pieces all over.

Replaced my Jumbo Jaws with Mega Jumbo Jaws. Spoiler: they're not 10^6 times as big. Nonetheless, they let me finish the bottom of this 12" dia bowl that had been sitting on the shelf. Swamp maple, cracked and spalted. #woodturning #woodworking

Borromean Rings. Oak. Each ring is an oval, about 4"x7". #woodworking

Jeff has said he'll win a majority of these bets. Smart people know he won't. 2/2

This ridiculous prediction is specific enough that someone should have asked Jeff to put his money where his mouth is, i.e. bet on it.
I (a vaccinated person) put $60 into the "pot", and Jeff puts $40. The $100 goes to me if I live to 2025, otherwise to Jeff. 1/2

Home welder here too. Auto-darkening helmet is a must for the beginner. Start with the MIG process on mild steel - more foolproof for the beginner. Later on you can aspire to the TIG process, and welding metals like aluminum and stainless steel.

Without disagreeing in the slightest, let me add:
The Buzzcocks
Stiff Little Fingers

My OGS and KGS ranks are 4k and 3k. We should play sometime.

Terry Bisson has the authoritative take on this issue:
web.archive.org/web/20190501...