Take an ordinary magic square and replace its numbers with resistors of the same ohmic value. Now the set of resistors in each row, column, and diagonal will yield the same total resistance value when joined together end to end.
This paramagic square, by Lee Sallows, is similar — except that the resistors must be joined in parallel:
From the ever-inventive Lee Sallows, a self-tiling tile set:
His article on such self-similar tilings appears in the December 2012 issue of Mathematics Magazine.
From Lee Sallows, a grid that inventories its own contents:
A devilish puzzle by Lee Sallows:
In the diagram above, nine numbered counters occupy the cells of a 3×3 checkerboard so as to form a magic square. Any 3 counters lying in a straight line add up to 15. There are 8 of these collinear triads.
Reposition the counters (again, one to each cell) to yield 8 new collinear triads, but now showing a common sum of 16 rather than 15.
From Lee Sallows, a geometric magic square:
The shards in each row and column produce a complete plate.
So do the diagonals!
Devised by Lee Sallows, each of these lists inventories its own contents:
In 1984, British engineer Lee Sallows built a dedicated computer to compose a self-enumerating pangram — a sentence that inventories its own letters. It succeeded:
This pangram contains four a’s, one b, two c’s, one d, thirty e’s, six f’s, five g’s, seven h’s, eleven i’s, one j, one k, two l’s, two m’s, eighteen n’s, fifteen o’s, two p’s, one q, five r’s, twenty-seven s’s, eighteen t’s, two u’s, seven v’s, eight w’s, two x’s, three y’s, & one z.
“Only the fool would take trouble to verify that his sentence was composed of ten a’s, three b’s, four c’s, four d’s, forty-six e’s, sixteen f’s, four g’s, thirteen h’s, fifteen i’s, two k’s, nine l’s, four m’s, twenty-five n’s, twenty-four o’s, five p’s, sixteen r’s, forty-one s’s, thirty-seven t’s, ten u’s, eight v’s, eight w’s, four x’s, eleven y’s, twenty-seven commas, twenty-three apostrophes, seven hyphens and, last but not least, a single !” — Lee Sallows
