Item 70, The chess problem "stolen from Chess for Fun, Chess for Blood" by Lasker is problem 66 from that book [1]. The problem as stated in the memo is wrong: the white bishop is on the eighth rank, not the seventh, so it should say Bishop on KB8, not on KB7. The problem in FEN is then:<p>5B2/6P1/1p6/8/1N6/kP6/2K5/8 w - - 1 1<p>The version from Lasker's book is <i>much</i> more interesting. It happens that the version from HAKMEM is also a mate-in-3, but kind of a mundane one, relative to Lasker's anyway.<p>[1] Lasker's book is on Google Books, and you can see the relevant page (page 145)
<a href="https://books.google.ca/books?id=y90UTQeLeeIC&pg=PA145" rel="nofollow">https://books.google.ca/books?id=y90UTQeLeeIC&pg=PA145</a> (spoiler: the solution is described on that page).
It's worth mentioning that many aspects of HAKMEM have found their way into "Hacker's Delight", one of the more impressive CS books ever published IMHO.<p><a href="http://www.hackersdelight.org/" rel="nofollow">http://www.hackersdelight.org/</a><p>See also Guy Steele's forward to the book, in which he talks about its relationship to HAKMEM.<p><a href="http://www.hackersdelight.org/foreword.pdf" rel="nofollow">http://www.hackersdelight.org/foreword.pdf</a>
There are a lot of pearls in this - I would call it lab book.<p>A while ago, I made a slow Clojure implementation of a generalized version of Bill Gospers continued fraction arithmetics from the HAKMEM<p><a href="http://github.com/timrichardt/stern-brocot-tree" rel="nofollow">http://github.com/timrichardt/stern-brocot-tree</a>
Interestingly, there's not only theorems but also conjectures in this list.<p>Interesting bit:<p><i>> ITEM 125 (Polya):</i><p><i>> CONJECTURE: If a function has a power series with integer coefficients and radius of convergence 1, then either the function is rational or the unit circle is a natural boundary.</i><p><i>> Reference: Polya, Mathematics and Plausible Reasoning, volume 2, page 46.</i><p>Has this conjecture been proved or disproved by now?
This is a classic. IMHO, HAKMEM should be required reading for everyone who programs computers. Likewise, everyone should own and read Hank Warren's <i>Hackers Delight</i>. For advanced practitioners, Knuth's <i>Art of Computer Programming</i> (particularly Volume 4) has some similar material. All explore the deep relationship between mathematics and programming.
Item 1 (expressing (p/q)! in terms of other (p/q)!) has no general solution still, as far as I know, but can easily be handled empirically for medium-sized n with the PSLQ algorithm.<p>Item 96 ("Solve go") can be made tractable by setting the board size to n=2.
<i>> Programs below this line are considered unfeasible.</i><p><a href="http://www.inwap.com/pdp10/hbaker/hakmem/proposed.html#item94" rel="nofollow">http://www.inwap.com/pdp10/hbaker/hakmem/proposed.html#item9...</a>