Xref: utzoo sci.math:9592 comp.misc:8118 rec.puzzles:5285
Path: utzoo!utgpu!jarvis.csri.toronto.edu!cs.utexas.edu!usc!snorkelwacker!spdcc!ima!haddock!karl
From: karl@haddock.ima.isc.com (Karl Heuer)
Newsgroups: sci.math,comp.misc,rec.puzzles
Subject: Re: Four 4's problem
Message-ID: <15842@haddock.ima.isc.com>
Date: 2 Feb 90 20:32:52 GMT
References: <5369@bgsuvax.UUCP> <1990Jan29.144925.13891@dvinci.usask.ca> <1990Feb1.124755.6966@planet.bt.co.uk>
Reply-To: karl@haddock.ima.isc.com (Karl Heuer)
Followup-To: rec.puzzles,sci.math
Organization: Interactive Systems, Cambridge, MA 02138-5302
Lines: 25
I'm removing comp.misc from followups, and adding rec.puzzles.
In article <1990Feb1.124755.6966@planet.bt.co.uk> tlj@planet.bt.co.uk (Tim Lennard-Jones) writes:
>>From article <5369@bgsuvax.UUCP>, by steiner@bgsuvax.UUCP (Ray Steiner):
>>>I believe that it was shown in the BENT of Tau Beta Pi not too long ago
>>>that 39 is the smallest integer that cannot be created this way. Is 39
>>>indeed the answer to the problem?
You have to be careful when quoting known results on this class of problem,
because the set of permissible operators isn't fixed. If you allow factorial,
floor, and square root, then I believe that *any* positive integer can be
generated from *one* four. (Or any other starting value larger than 2.)
>If this is so, perhaps someone could show me examples for 33 and 37.
The problem that started this thread permitted only +, -, *, /, and ^; I
presume that it's also okay to use parentheses for grouping, and to form
larger constants by juxtaposition ("44"). In this form, it appears that the
smallest positive unreachable integer is 11. (Yes: 33, 37, and 39 are also in
the list.)
Assuming that 39 was the correct answer for the problem as stated in the BENT,
what precisely must the question have been?
Karl Heuer karl@haddock.ima.isc.com rutgers!harvard!ima!haddock!karl