A magic square by Lee Sallows. The 16 pieces progress in area from 1 to 16, and those in each row, column, and long diagonal can be assembled to form the same target shape with area 34.
“Opus 34”
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Words and Numbers
In 1986 Lee Sallows invented the alphamagic square — spell out each number in this magic square and count its letters (25 -> TWENTY-FIVE -> 10), and you’ll produce another magic square:
David Brooks points out that this works also in Pig Latin.
Sallows extends the idea into geometry:
Alignment
By Lee Sallows: Assign the letters JHMLCNVTURISEYAPO to the integers -8 to 8 and you get:
And a reader points out that ERIS gives 10.
Pièce de Résistance
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:
Construction Set
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.
A Self-Intersecting Reflexicon
From Lee Sallows, a grid that inventories its own contents:
Counter Play
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.
“The Archaeologist’s Nightmare”
From Lee Sallows, a geometric magic square:
The shards in each row and column produce a complete plate.
So do the diagonals!
Bills of Lading
Devised by Lee Sallows, each of these lists inventories its own contents:
- fifteen e’s, seven f’s, four g’s, six h’s, eight i’s, four n’s, five o’s, six r’s, eighteen s’s, eight t’s, four u’s, three v’s, two w’s, three x’s
- sixteen e’s, five f’s, three g’s, six h’s, nine i’s, five n’s, four o’s, six r’s, eighteen s’s, eight t’s, three u’s, three v’s, two w’s, four x’s
The Quick Brown Fox …
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.