The problems
were published in *SIAM News* of Jan/Feb 2002, and later in
*Science* and elsewhere. The
answers
and winners have now been announced by the Challenge's organiser,
Prof. L. N.
Trefethen of Oxford Univ., and a write-up will appear in the July/Aug 2002
issue of *SIAM News*.

94 teams (of one to six members each, and from all across the world)
entered. Of these, 20 teams became joint winners by scoring a full
hundred points. Among those is the team that was formed in the
CompuServe SCIMATH forum,
an online discussion message board, and consisted of
__Brian Medley__ (*front, in the picture*),
Bernard B. Beard (*centre*),
and Marijke van Gans
(*me, at the back*).

That set the tone for our approach: each member of the budding team worked
individually on the problems. The hope was that once two of us had both done
the *same* problem without knowing the other's workings, we would not
have made the same mistakes and so be able to catch errors. The approach
paid off because that is exactly what happened, more than once.

This was not imposed in any way, we freely shared our workings for the asking, but each refrained from asking about those problems they thought they might still want to tackle themselves later. We did help each other with explanations of finer points of math, with algorithmic wrinkles, and references to resources.

Progress reports took place via the (public) message board. Only the bare digits though; any workings we eventually shared went via email. This compromise was deemed sufficient not to lead any lurkers in temptation of cribbing (as the Challenge would only accept answers with an indication of method used).

The team that coalesced in this way consisted of the three of us. We already knew each other (online, that is) from the forum, having joined it in the mid nineties. We worked on the problems off and on, other commitments permitting. The pace picked up again towards the deadline, when 5 finally yielded, and 10 and 8 became cliffhangers.

All our programs run on ordinary personal computers. No expensive math software packages were needed, and any techniques we didn't develop ourselves can be found freely on the web or in cheaply available standard works.

**1:** 0.323367431678
(*the integral of x*^{-1} cos(*x*^{-1} log *x*) )

Solution by Medley

**2:** 0.9952629194433541608903118094
(*the photon*)

Solution by v.Gans

Solution by Medley

**3:** 1.274224153
(*the norm of infinite matrix A*)

Solution by Medley

**4:** `-`3.3068686474752
(*the global minimum*)

Solution by v.Gans

Solution by Medley

**5:** 0.2143352346
(*the cubic closest to* 1/G )

Solution by v.Gans

**6:** 0.06191395447399
(*the flea*)

Solution by v.Gans

Solution by Medley

**7:** 0.7250783462684
(*the* 20,000² *matrix*)

Solution by Medley

5 digits & pic by v.Gans

**8:** 0.424011387034
(*the heat flow one*)

Solution by Beard

**9:** 0.78593367435
(*the integral with param* a)

Solution by Medley

**10:** 0.0000003837587979
(*the Brownian motion*)

Solution by v.Gans

Because of the requirement for high precision (usually, ten digits in the
result requires far more in the intermediate workings) only a few of our
programs were in C. Most were in
UBASIC, a number
theory oriented freeware BASIC by Prof. Yuji Kida of Rikkyo Univ., with many goodies, not just
high precision but also complex numbers, rationals, C style `+=` etc. etc.
Reassuringly, it uses *fixed* point fractions rather than floats. We used
version
8.74 for DOS. Later versions exist, for several platforms.

- This is the
`pdf`(0.5 Mb) we originally submitted for the contest, collated by Bernard Beard from our disparate`ASCII`and`HTML`write-ups,`*.UB`source, and`GIF`s (set zoom in Acrobat to 133.33% for the graphics). For each problem, in most cases, only one solution is included. - The web pages above show all these, but they have now had the
benefit of the relative calm past the deadline rush to allow some
light editing to zap confusing typos and unclear turns of phrase.
Remaining solutions have also been added, as well as some odds
& ends.
- This is the
`zip`(0.9 Mb) with all these web pages, and their graphics, and bits & bobs.

J. Boersma,
J.K.M. Jansen, F.H. Simons, F.W. Steutel

Folkmar Bornemann

Michel Kern

Dirk Laurie

Peter Robinson

Peter Simon and Kim McInturff

Stan Wagon & Danny Kaplan

(some of these are people's homepages, follow the relevant link on the page).

URL of this page: http://www.maxwellian.demon.co.uk/~marijke/SIAM2002/ (this version was updated 15 June 2002)