triangle ellipse

so a labeled triangle defines an ellipse...

stapler

A stapler with a extra-staples holder.

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Information bits in permutations

perl -lwe 'for $i ( 1 .. 10 ) { for $j ( 1 , $i .. $i + 3 ) { $v = $i * $j ; $s = 0 ; for ( 1 .. $v ) { $s += log ( $_ ) } $s /= log ( 2 ) ; print "$v $s" } }' | sort -nu

1	0
2	1
3	2.58496250072116
4	4.58496250072116
5	6.90689059560852
6	9.49185309632968
7	12.2992080183873
8	15.2992080183873
9	18.4691330198296
10	21.791061114717
12	28.8354552340754
15	40.2501404698826
16	44.2501404698826
18	52.5075283125753
20	61.0773839209062
24	79.0376574191005
25	83.6815136088752
28	97.9441957512373
30	107.709067341973
35	132.924403629914
36	138.094328631356
40	159.159039824179
42	169.908909251575
48	202.9495720297
49	208.564281873815
54	237.063811080429
56	248.652525716012
63	289.995143941724

256 bits

Let m=2^256.

57! < m < 58! (Let 58 people in a ring remember who they stood next to?)

(Note: 2^224 < 52! < 2^225 for permutations of a deck of cards.)

2^256 is approximately 10^77.

55 letters of the alphabet

Choosing, in any order, 131 items out of 262.

Choosing, in order, 26 items out of 933 (=31*31).

sudoku and the game of go

trying to define the bounds of "purely by logic, no guessing required" for sudoku, and reasoning about go 囲碁 positions seem like similar computational pursuits.

greasemonkey first attempt

fark cleaning userscript (diveintogreasemonkey is a good reference.)

shrinking packed objects

Consider a set of objects, say discs, packed on a plane, and (some or all) of the distances between the centers of the discs. Let one of the discs shrink, in place. Under what conditions can the ensemble be rearranged so that none of the distances increase? (Insipired from layout of standard cells of conservative gate sizes.)

String tree

Is there a dense mapping from strings to trees, such that every possible string maps to a tree, and vice versa?

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reverse BW

What happens if you uncompress random bits with an English trained entropy decoder, MTF, and Burrows Wheeler? Maybe try symbols that stand for words instead of individual characters.

bnsp

The converse of non-breaking space nbsp, a breaking non-space, handled by search engines, justifiers, ligatures, kerning, correctly.

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mmporg computer

With a MMOG-like network of thousands of thousands of processors and humans, what could you compute?

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pi in base 79

digits are 0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~

fortunately the decimal point is not among the digits.

3.;>egIm`:=_c3E>}c]f4r5He@DfV<TP<04h>8;tq1MFlFfvYv9ZSn|9yX6|2^AV? <h`W^mKp\25a[aFlS:\uLPq<YIzwjM}afXC] Kv|=VqEZmR\D`I=~dM2f6Q9WY?rHbb7h7[_?[RBP=k:SC

see also pi in base 72.

echo 'obase=79; scale=2000; 4*a(1)' | bc -l | perl -pwe 's/\\\n//;s/\./ /' | perl -plwae '$_=""; for$i(@F) {$_.=chr($i+48)} s/^(.)/$1./'

sqrt(2) begins 1.Pi

More Sudoku thoughts

Since generalized Sudoku is NP-complete, it should be possible to rewrite the Certicom or rsa challenges to "solve this sudoku to win a hundred thousand dollars."

Takayuki YATO, Takahiro SETA, Complexity and Completeness of Finding Another Solution and Its Application to Puzzles

16x16 hypercube (4D cube) with numbers written in corner-shaded binary is elegant. Consider hints of just some of the bits of a number.

Permutation count

Given a permutation of N different objects, map it uniquely to an integer from 0 to N!-1, and vice versa. Variable-base number system. (factorial).

Books

What do we need books for these days?

1. "Emergency" situations which electricity and/or network might be unavailable. 2. Pictures: print resolution is much higher than screen resolution. One example: font collections.

Generally not for text, as books cannot be rapidly searched or use hyperlinks.

Cycle times and frequencies

10 MHz = 100 ns

20 MHz = 50 ns

50 MHz = 20 ns

100 MHz = 10 ns

200 MHz = 5 ns

500 MHz = 2 ns

1 GHz = 1000 ps

2 GHz = 500 ps

5 GHz = 250 ps

10 GHz = 100 ps

20 GHz = 50 ps

50 GHz = 20 ps

100 GHz = 10 ps

200 GHz = 5 ps

500 GHz = 2 ps

1 THz = 1 ps

sudoku 3

with the constraint that each 9-box position, eg center square, contains no duplicates, are there sudoku solutions? Equivalently, four orthogonal planes through each point of a 3x3x3x3 four-dimensional hypercube contains the numbers 1 through 9. Hmm, it looks like there are actually six orthogonal planes (4 choose 2).

sudoku combinations

One can search the web for the number 27704267971 to find information about sudoku.

Restart continue

There ought to be an easy way to set up processes that checkpoint and start again after reboot (Seti@home).

64 characters from zero

0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnop

Repeated Burrows-Wheeler

hello.world
olhdrellwo.
ohrloelw.dl
w.oordellhl
wrdlleh.ool
hrleldoo.wl
olllerwodh.
holdllow.er
wl.rodlhleo
lollwhdre.o
ehrwooll.dl
l.leldoowhr
lllwre.doho
e.roolldhwl
elldlwoor.h
rlh.ledwool
hell.roowld
llhdlwero.o
ohwllodr.el
ro.owlelldh
olldlwer.ho
rlw.lodohel
woho.erldll
ol.ordlhwel
lrwlodel.oh
lodoewhl.lr
loowhr.ldle
rllw.deloho
w.dorellhol
w.rlleohdol
whlolroed.l
deowho.rlll
oldwllrhe.o
elhrowlo.ld
oldl.ewlrho
ll.rdowohle
lrlolhewd.o
dwhlorol.le
lelwo.hrlod
ool.drewlhl
l.rlowholde
lldweorhl.o
llwrhlo.eod
oo.rdhllewl
orldlhwol.e
ll.lordweoh
lrwolh.elod
ho.loedlwlr
oeor.wdhlll
rwodhllleo.
ooldllhew.r
wlhloldor.e
rl.lowhldoe
llowrh.dleo
h.lrdolelwo
hrloo.ewdll
ow.lldrolhe
wlhllo.redo
oerlwhlld.o
dlowlhro.el
ol.lewdrlho
lwllo.rohde
ohdowlelr.l
rhlow.eldlo
wl.redhlloo
lerdwhllo.o
orlwohll.ed
le.olhrwdol
ewllloo.dhr
o.rdwllolhe
orhlowlel.d
l.lrewhdloo
lhrwod.olle
dollleow.hr
wrl.llodeho
loder.llhwo
rodll.olweh
loweldor.hl
rlw.ehldloo
wl.ehdrlool
lh.ewrooldl
hl.loldorwe
llweho.ldor
olwe.rlhdol
ehwlroodl.l
loled.worlh
dellorhlwo.
o.drelhwlol
o.rleowlldh
olldlrwhe.o
elhwlodo.lr
oorlew.dllh
w.llrldhooe
wlodr.lohle
rolohw.llde
wldol.olreh
llreowod.lh
dorl.hlwelo
low.rehldol
wlreholdl.o

ECM test target

? a=1;for(i=1,16,a=a*nextprime(i*10^18))

? log(a)/log(2)

%6 = 1000.965431797442978101766016

20922789888000002194246730188800098622571843019522526044727022284713263491595253079767428738692325860932989068218738520867301352625799317614888032706199405063395128478393921924020284089574414059141111378674790274174706841130275649554622979423900596132415641067351925357639595115173010430109392057073763