| T.R | Title | User | Personal
Name | Date | Lines |
|---|
| 525.1 | | CLT::GILBERT | Juggler of Noterdom | Fri Jun 27 1986 02:24 | 5 |
| > If you add any positive integer to the integer formed by reversing
> the digits, then do the same thing with the sum, and keep repeating,
> you will eventually reach a sum that is palindromic.
Really?? Lynn should be able to comment on this.
|
| 525.2 | re. .1 Not allways... | THEBUS::KOSTAS | Kostas G. Gavrielidis <o.o> | Fri Jun 27 1986 09:57 | 9 |
| re. .1
Well,
this does not work allways as you can tell by some of the problems
listed in .0.
Kostas G.
|
| 525.3 | | AURORA::HALLYB | Free the quarks! | Fri Jun 27 1986 10:56 | 2 |
| I believe you \can/ disprove the "eventually palindromic" hypothesis
for binary arithmetic. I think the problem is still open for decimal.
|
| 525.4 | | CLT::GILBERT | Juggler of Noterdom | Sun Jun 29 1986 04:17 | 10 |
| Can we prove that for numbers > 4 digits in length, the first palindromic
number never occurs as a result of a 'carry' (that is, when the number
grows another digit in length).
Is it possible to construct a number of the form:
def000000ghi000000jkl
that evolves to:
abc000000def000000ghi000000jkl000000mno
such that we can assert that the number never becomes palindromic?
|
| 525.5 | Base 2 numbers which do not reach palindromes ... | THEBUS::KOSTAS | Kostas G. Gavrielidis <o.o> | Wed Jul 09 1986 10:11 | 14 |
| re. .3
Yes, in base 2, it is not difficult to contruct integers which do
not reach palindromes. Here is a such an integer 10110 .
For more details on this consult the book:
Recreation in Mathematics, by R. P. Sprague
(London: Blackie and Son, Ltd., 1963)
Enjoy,
Kostas G.
|
| 525.6 | solution to problem 1 of .0 | THEBUS::KOSTAS | Kostas G. Gavrielidis <o.o> | Wed Jul 09 1986 10:51 | 19 |
| re. .0
Solution to problem 1.
> Problem 1: Find an integer other than 89 that requires 24
> steps to reach a palindromic sum.
If an integer n reaches a palindromic sum in m steps,
then the integer formed by reversing the digits of n also
reaches a palindromic sum in m steps. (Why?).
So 98 reaches a palindromic sum in 24 steps.
Enjoy,
Kostas G.
|
| 525.7 | solution to problem 5 of .0 by CALREAL | THEBUS::KOSTAS | Kostas G. Gavrielidis <o.o> | Fri Jul 11 1986 23:52 | 22 |
| re. .0
Solution to Problem 5 of .0 by CALReal
>
> Problem 5: What are the palindromic primes less than 10,000.
>
CALREAL> palindromic primes up to ( 1000 );
2 3 5 7 11 101
131 151 181 191 313 353
373 383 727 757 787 797
919 929
There were: 20 palindromic prime(s)
Enjoy,
Kostas G.
|
| 525.8 | | CLT::GILBERT | $ no /nono vaxnotes | Sat Jul 12 1986 11:26 | 12 |
| And there are 93 5-digit palindromic primes.
10301,10501,10601,11311,11411,12421,12721,12821,13331,13831
13931,14341,14741,15451,15551,16061,16361,16561,16661,17471
17971,18181,18481,19391,19891,19991,30103,30203,30403,30703
30803,31013,31513,32323,32423,33533,34543,34843,35053,35153
35353,35753,36263,36563,37273,37573,38083,38183,38783,39293
70207,70507,70607,71317,71917,72227,72727,73037,73237,73637
74047,74747,75557,76367,76667,77377,77477,77977,78487,78787
78887,79397,79697,79997,90709,91019,93139,93239,93739,94049
94349,94649,94849,94949,95959,96269,96469,96769,97379,97579
97879,98389,98689
|
| 525.9 | CTRL/Z | AURORA::HALLYB | Free the quarks! | Mon Jul 14 1986 13:40 | 1 |
| Does anybody have a badge number that is a palindromic prime?
|
| 525.10 | I know but I'm not telling. | MODEL::YARBROUGH | | Mon Jul 14 1986 15:17 | 2 |
| Aside from Ken Olsen's no. 1, yes, there are palindromic prime badge
numbers currently active. It is inappropriate to list any here.
|
| 525.11 | there are 781 palindomic primes < than 10,000,000 | THEBUS::KOSTAS | Kostas G. Gavrielidis <o.o> | Tue Jul 15 1986 09:34 | 144 |
| Well,
There are 781 palindromic primes less than 10,000,000
CALREAL> palindromic primes up to ( 10000000 );
2 3 5 7 11 101
131 151 181 191 313 353
373 383 727 757 787 797
919 929 10301 10501 10601 11311
11411 12421 12721 12821 13331 13831
13931 14341 14741 15451 15551 16061
16361 16561 16661 17471 17971 18181
18481 19391 19891 19991 30103 30203
30403 30703 30803 31013 31513 32323
32423 33533 34543 34843 35053 35153
35353 35753 36263 36563 37273 37573
38083 38183 38783 39293 70207 70507
70607 71317 71917 72227 72727 73037
73237 73637 74047 74747 75557 76367
76667 77377 77477 77977 78487 78787
78887 79397 79697 79997 90709 91019
93139 93239 93739 94049 94349 94649
94849 94949 95959 96269 96469 96769
97379 97579 97879 98389 98689 1003001
1008001 1022201 1028201 1035301 1043401 1055501
1062601 1065601 1074701 1082801 1085801 1092901
1093901 1114111 1117111 1120211 1123211 1126211
1129211 1134311 1145411 1150511 1153511 1160611
1163611 1175711 1177711 1178711 1180811 1183811
1186811 1190911 1193911 1196911 1201021 1208021
1212121 1215121 1218121 1221221 1235321 1242421
1243421 1245421 1250521 1253521 1257521 1262621
1268621 1273721 1276721 1278721 1280821 1281821
1286821 1287821 1300031 1303031 1311131 1317131
1327231 1328231 1333331 1335331 1338331 1343431
1360631 1362631 1363631 1371731 1374731 1390931
1407041 1409041 1411141 1412141 1422241 1437341
1444441 1447441 1452541 1456541 1461641 1463641
1464641 1469641 1486841 1489841 1490941 1496941
1508051 1513151 1520251 1532351 1535351 1542451
1548451 1550551 1551551 1556551 1557551 1565651
1572751 1579751 1580851 1583851 1589851 1594951
1597951 1598951 1600061 1609061 1611161 1616161
1628261 1630361 1633361 1640461 1643461 1646461
1654561 1657561 1658561 1660661 1670761 1684861
1685861 1688861 1695961 1703071 1707071 1712171
1714171 1730371 1734371 1737371 1748471 1755571
1761671 1764671 1777771 1793971 1802081 1805081
1820281 1823281 1824281 1826281 1829281 1831381
1832381 1842481 1851581 1853581 1856581 1865681
1876781 1878781 1879781 1880881 1881881 1883881
1884881 1895981 1903091 1908091 1909091 1917191
1924291 1930391 1936391 1941491 1951591 1952591
1957591 1958591 1963691 1968691 1969691 1970791
1976791 1981891 1982891 1984891 1987891 1988891
1993991 1995991 1998991 3001003 3002003 3007003
3016103 3026203 3064603 3065603 3072703 3073703
3075703 3083803 3089803 3091903 3095903 3103013
3106013 3127213 3135313 3140413 3155513 3158513
3160613 3166613 3181813 3187813 3193913 3196913
3198913 3211123 3212123 3218123 3222223 3223223
3228223 3233323 3236323 3241423 3245423 3252523
3256523 3258523 3260623 3267623 3272723 3283823
3285823 3286823 3288823 3291923 3293923 3304033
3305033 3307033 3310133 3315133 3319133 3321233
3329233 3331333 3337333 3343433 3353533 3362633
3364633 3365633 3368633 3380833 3391933 3392933
3400043 3411143 3417143 3424243 3425243 3427243
3439343 3441443 3443443 3444443 3447443 3449443
3452543 3460643 3466643 3470743 3479743 3485843
3487843 3503053 3515153 3517153 3528253 3541453
3553553 3558553 3563653 3569653 3586853 3589853
3590953 3591953 3594953 3601063 3607063 3618163
3621263 3627263 3635363 3643463 3646463 3670763
3673763 3680863 3689863 3698963 3708073 3709073
3716173 3717173 3721273 3722273 3728273 3732373
3743473 3746473 3762673 3763673 3765673 3768673
3769673 3773773 3774773 3781873 3784873 3792973
3793973 3799973 3804083 3806083 3812183 3814183
3826283 3829283 3836383 3842483 3853583 3858583
3863683 3864683 3867683 3869683 3871783 3878783
3893983 3899983 3913193 3916193 3918193 3924293
3927293 3931393 3938393 3942493 3946493 3948493
3964693 3970793 3983893 3991993 3994993 3997993
3998993 7014107 7035307 7036307 7041407 7046407
7057507 7065607 7069607 7073707 7079707 7082807
7084807 7087807 7093907 7096907 7100017 7114117
7115117 7118117 7129217 7134317 7136317 7141417
7145417 7155517 7156517 7158517 7159517 7177717
7190917 7194917 7215127 7226227 7246427 7249427
7250527 7256527 7257527 7261627 7267627 7276727
7278727 7291927 7300037 7302037 7310137 7314137
7324237 7327237 7347437 7352537 7354537 7362637
7365637 7381837 7388837 7392937 7401047 7403047
7409047 7415147 7434347 7436347 7439347 7452547
7461647 7466647 7472747 7475747 7485847 7486847
7489847 7493947 7507057 7508057 7518157 7519157
7521257 7527257 7540457 7562657 7564657 7576757
7586857 7592957 7594957 7600067 7611167 7619167
7622267 7630367 7632367 7644467 7654567 7662667
7665667 7666667 7668667 7669667 7674767 7681867
7690967 7693967 7696967 7715177 7718177 7722277
7729277 7733377 7742477 7747477 7750577 7758577
7764677 7772777 7774777 7778777 7782877 7783877
7791977 7794977 7807087 7819187 7820287 7821287
7831387 7832387 7838387 7843487 7850587 7856587
7865687 7867687 7868687 7873787 7884887 7891987
7897987 7913197 7916197 7930397 7933397 7935397
7938397 7941497 7943497 7949497 7957597 7958597
7960697 7977797 7984897 7985897 7987897 7996997
9002009 9015109 9024209 9037309 9042409 9043409
9045409 9046409 9049409 9067609 9073709 9076709
9078709 9091909 9095909 9103019 9109019 9110119
9127219 9128219 9136319 9149419 9169619 9173719
9174719 9179719 9185819 9196919 9199919 9200029
9209029 9212129 9217129 9222229 9223229 9230329
9231329 9255529 9269629 9271729 9277729 9280829
9286829 9289829 9318139 9320239 9324239 9329239
9332339 9338339 9351539 9357539 9375739 9384839
9397939 9400049 9414149 9419149 9433349 9439349
9440449 9446449 9451549 9470749 9477749 9492949
9493949 9495949 9504059 9514159 9526259 9529259
9547459 9556559 9558559 9561659 9577759 9583859
9585859 9586859 9601069 9602069 9604069 9610169
9620269 9624269 9626269 9632369 9634369 9645469
9650569 9657569 9670769 9686869 9700079 9709079
9711179 9714179 9724279 9727279 9732379 9733379
9743479 9749479 9752579 9754579 9758579 9762679
9770779 9776779 9779779 9781879 9782879 9787879
9788879 9795979 9801089 9807089 9809089 9817189
9818189 9820289 9822289 9836389 9837389 9845489
9852589 9871789 9888889 9889889 9896989 9902099
9907099 9908099 9916199 9918199 9919199 9921299
9923299 9926299 9927299 9931399 9932399 9935399
9938399 9957599 9965699 9978799 9980899 9981899
9989899
There were: 781 palindromic prime(s)
Enjoy,
Kostas G.
|
| 525.12 | F10 | AURORA::HALLYB | Free the quarks! | Tue Jul 15 1986 11:26 | 21 |
| Regarding palindromic prime badge numbers -- one doesn't have to
associate a name with the badge ("that would be telling").
[1] What's the smallest palindromic prime active badge number?
Hint: 1 is _not_ _prime_.
[2] What's the largest?
I don't know the answers to [1] or [2], though some reader might.
Notice that there are no 6-digit candidates, so the lucky owner
of badge 98689 (if still employed) would be the winner here.
In fact, aside from 11 there are no palindromic primes with an even
number of digits in any of the lists given thus far.
[3] Prove there is only one palindromic prime containing an even
number of digits, base 10.
Will the "pros" please lay off this one, let some new blood try.
[4] How does [3] extend to other number bases?
|
| 525.13 | New blood | GNERIC::QUAYLE | | Tue Jul 15 1986 15:09 | 15 |
| Suppose there is a palindromic prime with 2n digits, call it p.
Since p is a palindromic number with an even number of digits, the
digit at position i is the same as the digit at position 2n+1-i,
where i ranges from 1<->n.
i and 2n+1-i always have opposite parity.
.: for a palindromic number with an even number of digits,
(sum of digits in odd positions) = (sum of digits in even pos.)
since i and 2n+1-i will always never be in the same summation.
They will always go in opposite summations and cancel each other.
.: Every palindromic number with an even number of digits is divisible
by 11, so cannot be prime.
|
| 525.14 | largest prime palindromic badge no. | MODEL::YARBROUGH | | Wed Jul 16 1986 09:22 | 1 |
| Badge 98689 is currently active.
|
| 525.15 | A sniglet... | MODEL::YARBROUGH | | Wed Jul 16 1986 09:24 | 1 |
| Aibohphobia : fear of palindromes.
|
| 525.16 | re. .0 solution to problem 6 in .0 | THEBUS::KOSTAS | Kostas G. Gavrielidis <o.o> | Wed Jul 16 1986 11:00 | 22 |
| re. .0
solution to the problem 6 in .0
> Problem 6: Show that there are no four-digit palindromic primes.
Any four-digit palindrome can be expressed in the form
a + 10b + 100b + 1000a = 11 ( 91a +10b )
where a >= 0 and b >= 0 are integers.
Hense, 11 divides every four-digit palindrome.
This proof is easily extented to show that every palindrome having
an even number of digits is divisible by 11.
Enjoy,
Kostas G.
|
| 525.17 | not the largest, probably | OBLIO::SHUSTER | Red Sox Addition: 1986 = 1975 + 1 | Wed Jul 16 1986 12:15 | 8 |
|
> Badge 98689 is currently active.
So are plenty of badges with six digits.
-Rob
|
| 525.18 | Look again. | CLOUD::SHIRRON | Stephen F. Shirron, 223-3198 | Wed Jul 16 1986 13:07 | 6 |
| Re .17:
Apparently you failed to notice that there are NO six digit palendromic
primes. And there are not yet any seven digit badge numbers.
stephen
|
| 525.19 | re. .15 | THEBUS::KOSTAS | Kostas G. Gavrielidis <o.o> | Fri Jul 18 1986 14:37 | 11 |
| re. .15
> Aibohphobia : fear of palindromes.
Hm!
I thought this may be more appropriate
PalindromicimordnilaPhobia
|
| 525.20 | I'll cast a vote | CACHE::MARSHALL | beware the fractal dragon | Fri Jul 18 1986 16:58 | 6 |
|
I kinda like Aibohphobia
although anyone with this problem would have a hard time
hearing the psychiatrist tell them the name of their condition :-)
sm
|
| 525.21 | Hm! | THEBUS::KOSTAS | Kostas G. Gavrielidis <o.o> | Fri Jul 18 1986 17:26 | 9 |
| re. .20
ok then if Aibohphobia is to mean fear (phobia) of palindomes
what will then fear of fear be? phobiaphobia ?
and what will then fear of reverse fear be? phobiaibohp ?
|
| 525.22 | raef|fear | CACHE::MARSHALL | beware the fractal dragon | Mon Jul 21 1986 12:09 | 12 |
| re .21:
> fear of fear: phobiaphobia
sounds good to me.
> fear of reverse fear: phobiaibohp
reverse fear? I assume you don't mean the antonym of "fear" {phobia}.
sm
|
| 525.23 | | CLT::GILBERT | Was Winston Churchill a phobiaphobiac? | Mon Jul 21 1986 13:02 | 0 |
| 525.24 | | ERIS::CALLAS | Jon Callas | Mon Jul 21 1986 16:37 | 3 |
| The fear of fear is phobophobia.
Jon
|
| 525.25 | To paraphrase FDR, | AURORA::HALLYB | Free the quarks! | Mon Jul 21 1986 17:54 | 1 |
| "Our only problem is phobophobia."
|
| 525.26 | | CLT::GILBERT | eager like a child | Mon Aug 11 1986 15:25 | 1 |
| See also the Frank and Ernest comic strip in Sunday's Nashua Telegraph.
|
| 525.27 | 196? There's something wrong with that number! | ZFC::DERAMO | Daniel V. D'Eramo | Wed Nov 25 1987 12:24 | 15 |
| Re: .0
>> Problem 8: Explain how one can establish that the integer 196
>> does not reach a palindromic sum within 1,000 steps.
[Where a "step" consists of reversing the digits of a number and
then adding that to the original number.]
I submitted a background job running at priority one that has
already gone 5000 steps starting with 196 without reaching a
palindrome.
Presumably the author of .0 was looking for a more clever solution!
Dan
|
| 525.28 | | CLT::GILBERT | Builder | Wed Nov 25 1987 17:59 | 23 |
| If an addition that increases the length of the number results in a palindrome,
then each of the digits in the palindrome is either 0, 1, or 2.
Suppose the addition is:
c[n+1] c[n] c[n-1] ... c[ 1 ] c[0]
x[n] x[n-1] ... x[ 1 ] x[0]
+ x[0] x[ 1 ] ... x[n-1] x[n]
---------------------------------------
y[n+1] y[n] y[n-1] ... y[ 1 ] y[0]
Where the 'c's are carries. We are given that c[0] = 0, and c[n+1] = 1,
and y[i] = y[n+1-i]. Also, x[i] + x[n-i] + c[i] = 10*c[i+1] + y[i], so that:
x[(n-i)] + x[n-(n-i)] + c[(n-i)] = 10*c[(n-i)+1] + y[(n-i)]
=> x[n-i] + x[i] + c[n-i] = 10*c[n+1-i] + y[n-i]
=> x[i] + x[n-i] = 10*c[n+1-i] - c[n-i] + y[n-i]
=> x[i] + x[n-i] = 10*c[n+1-i] - c[n-i] + y[i+1]
= 10*c[i+1] - c[i] + y[i],
=> y[i+1] = 10*(c[i+1] - c[n+1-i]) + c[n-i] - c[i] + y[i]
We can use this and an induction to show that y[i] = c[i+1] + c[i], and
c[i+1] = c[n+1-i], for all i.
|
| 525.29 | Dan's Last Theorem? | ZFC::DERAMO | Daniel V. D'Eramo | Mon Nov 30 1987 12:25 | 14 |
| I have discovered a truly marvelous proof that the sequence of
numbers generated this way starting from 196 will not cycle in
less than N steps where N is:
17.2953...
e
e
e
e
e
Unfortunately, the proof is too large to fit in the margin.
Dan
|
| 525.30 | Pity Fermat didn't have NOTES | SQM::HALLYB | Profitus Interruptus | Mon Nov 30 1987 13:28 | 8 |
| > Unfortunately, the proof is too large to fit in the margin.
Try "DO" SET RIGHT_MARGIN 888
Also, are you sure about that 17.2953??? My calculator shows that
SQRT(300) = 17.3205...
Just wondering,
|
| 525.31 | | CLT::GILBERT | Builder | Mon Nov 30 1987 17:51 | 7 |
| The following might be used to find numbers that never yield a palindrome.
Consider the first and last K digits in the number, and look at the
digits in the sum (note that there may be a carry into the high part).
If these can't be part of a palindrome, continue the process. Hopefully,
this tree search will always result in cycles, and never result in a
possible palindrome.
|
| 525.32 | Wow! Amazing! | ZFC::DERAMO | Daniel V. D'Eramo | Mon Nov 30 1987 18:46 | 11 |
| Re .-1
>> If these can't be part of a palindrome, continue the process.
>> Hopefully, this tree search will always result in cycles, and never
>> result in a possible palindrome.
I have extended my proof to show that not just 196, but no positive
integer with less than approx. 10^517 digits, can be the first number
of a cycle of n -> n+reverse(n).
Dan
|
| 525.33 | It's been done, sort of... | AKQJ10::YARBROUGH | Why is computing so labor intensive? | Tue Dec 01 1987 08:39 | 8 |
| Lest anyone (else) waste an inordinate amount of computer time on the
problem, I have run the 196 case out to 75,000 cycles without forming a
palindrome. (Aren't microvaxen fun?)
If someone wants an interesting problem in this space that is still very
much open, check out note 95.
Lynn
|
| 525.34 | Well, it seemed funny at the time. | ZFC::DERAMO | Daniel V. D'Eramo | Tue Dec 01 1987 18:32 | 36 |
| Re: .29
>> I have discovered a truly marvelous proof that the sequence of
>> numbers generated this way starting from 196 will not cycle in
>> less than N steps where N is:
Re: .32
>> I have extended my proof to show that not just 196, but no positive
>> integer with less than approx. 10^517 digits, can be the first number
>> of a cycle of n -> n+reverse(n).
Okay, I can now fit the proofs in the margins. :-)
Let n be a positive integer, and let reverse(n) be the
number you get by writing n in base 10 and reversing the
digits. Define f(n) to be n+reverse(n) and consider the
sequence n, f(n), f(f(n)), ...
reverse(n) > 0
n + reverse(n) > n
f(n) > n
This means that n < f(n) < f(f(n)) < ... -- the sequence
cannot cycle.
In .29 I phrased this as no cycles starting with n=196 will
occur in the first N steps for some outrageous N. In .32 I
phrased it as no cycles starting from n's with less than
10^517 digits. But really there are no cycles, period. :^)
The sequences can stop at a palindrome or they can diverge to
positive infinity, but they will never cycle.
Dan
|
| 525.35 | 196: it takes a licking, and keeps on ticking | AITG::DERAMO | Dan D'Eramo, nice person | Sat Feb 17 1990 21:35 | 42 |
| >> .0 Problem 8: Explain how one can establish that the integer 196
>> does not reach a palindromic sum within 1,000 steps.
Path: shlump.nac.dec.com!decuac!haven!ames!think!samsung!cs.utexas.edu!uunet!mcsun!ukc!servax0!sersun2!alan
From: [email protected] (Stanier A)
Newsgroups: sci.math
Subject: Re: Palindromic Numbers
Message-ID: <[email protected]>
Date: 16 Feb 90 11:40:31 GMT
References: <[email protected]> <[email protected]>
Sender: [email protected]
Reply-To: [email protected]
Organization: University of Essex, Colchester, UK
Lines: 27
In <[email protected]> [email protected] (David Paterson) writes:
}
}> I remember reading once about the process of forming such numbers from
}> any integer by sucessively reversing the digits of the integer and
}> adding. For example, the number 23 is a 1-step palindrome: 23 + 32 =
}> 55. The number 28 is a 2-step palindrome: 28 + 82 = 110; 110 + 011 =
}> 121.
}>
}> In general, what statements can be made about any integer X, the
}> palindrome it eventually processes into (Xp), and n, the number of
}> steps required to reach Xp? Is it provable that X -> Xp for all
}> positive integers?
}
}Too hard. Tried this over the weekend and got absolutely nowhere.
}Here's a sub-problem. If the starting integer X is 196 then do you
}eventually get a palindrome ?
}
}I tracked this on computer for 24,094 steps and all I can say is that
}if Xp exists then it has more than 10,000 digits.
I have a program permanently doing this, running as the lowest-priority job
on one of our machines. The last time it e-mailed me, it had taken
5754000 steps, reaching a non-palindromic integer of 2382370 digits.
It's still running. If it ever finishes, I'll post the results.
--
Alan M Stanier | email [email protected] | tel +44 206-872153 | fax +44 206-860585
|
| 525.36 | re .-1 I think you broke the record ... | OINOH::KOSTAS | He is great who confers the most benefits. | Sun Feb 25 1990 17:59 | 16 |
| re .-1
you may have broken the record. The only other time that the number 196
was put to the test was in 1972 by Rebmann and Sentyrz in 1972 and they
only wend as far as 10,000 steps (ref. "A note on palindromes by
reversal-addition" Mathematics Magazine 45(1972):186-187), but they did
this to 74 other integers (i.e. 196, 879, 1997, 7059, 9999, ... ,
90379, 90579, 99999). These 74 were reduced from the 6091 given by Trigg
as numbers which lead to no palindroms with fewer than 201-to-3710 digits.
I would like to see how far we can go with some of these 74 other
numbers.
Enjoy,
Kostas
|
| 525.37 | | AITG::DERAMO | Dan D'Eramo, nice person | Mon Feb 26 1990 15:22 | 15 |
| re .-1
>> -< re .-1 I think you broke the record ... >-
>>
>> re .-1
>> you may have broken the record.
The author of the article posted in .35 is at the
University of Essex (according to the article) and
so won't be able to respond to you.
The way you phrased .-1 I wasn't sure if you thought it
was me.
Dan
|