Colorful "polar stratospheric clouds"

As reported by Spaceweather.com:

For the third day in a row, Arctic sky watchers are reporting a widespread outbreak of polar stratospheric clouds. "The colors are spectacular," says Ramune Sapailaite, who photographed the display over Gran, Norway..."The clouds were visible in the sky all day, but the colors really exploded just before sunset," says Sapailaite. "I took these pictures using my cellphone."

Widely considered to be the most beautiful clouds on Earth, polar stratospheric clouds (PSCs) are rare. Earth's stratosphere is very dry and, normally, it has no clouds at all. PSCs form when the temperature in the Arctic stratosphere drops to a staggeringly-low -85 C. Then, and only then, can widely-spaced water molecules begin to coalesce into tiny ice crystals. High-altitude sunlight shining through the crystals creates intense iridescent colors that rival auroras.

Related:  Fire rainbow and circumhorizotal arc.  There's probably additional information somewhere at Atmospheric Optics.

Some "15" puzzles are unsolvable

The example shown, posted on the puzzles subreddit, is on a watch.  What I remember are the old "analog" versions with small sliding wooden pieces in a frame.  I used to get great satisfaction as a child by solving scrambled puzzles.  What I learned this morning is that the puzzles date back way before my time:

The puzzle was "invented" by Noyes Palmer Chapman, a postmaster in Canastota, New York, who is said to have shown friends, as early as 1874, a precursor puzzle consisting of 16 numbered blocks that were to be put together in rows of four, each summing to 34 (see magic square)... The game became a craze in the U.S. in 1880...

Some later interest was fueled by [Sam] Loyd's offer of a $1,000 prize (equivalent to $34,996 in 2024) to anyone who could provide a solution for achieving a particular combination specified by Loyd, namely reversing the 14 and 15, which Loyd called the 14-15 puzzle. This is impossible, as had been shown over a decade earlier by Johnson & Story (1879), because it requires a transformation from an even to an odd permutation.

The Reddit thread confirms that the one illustrated is unsolvable, which is confirmed at the Wikipedia entry.  In fact, half of all initial states of the puzzle will be mathematically impossible to resolve.  To guarantee solvability, a puzzle would need to be manufactured with the pieces "solved" and then scrambled before distribution (or by asking the end-user to do so).  I'm glad all my childhood versions were solvable.

When you microwave an ice cube...

... the results are somewhat unexpected.

I had heard that solid ice does not respond to microwaves the way water does, so today while boiling some water for ramen, I also put in the (standard suburban) microwave one ice cube (with a paper towel to catch any meltwater).

The paper towel was unnecessary.  After 2 1/2 minutes the water in the measuring cup was in a full rolling boil, but the ice cube was ice cold.  There wasn't even a drop of water on the towel beneath.

Posting this so readers can use the info to win bar bets or impress your children at dinner.  Or perhaps next time you host a party ask guests to guess "how quickly" will the microwave melt the ice cube.  

Addendum:  several interesting observations in the comment thread.

Related:  Microwaving Ice - why defrosting is so slow.  Note: "This is why you shouldn't defrost a chicken on full power..."