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Enigma 1737 - Base jumping
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Chappy
Apr 4, 2013, 1:18:48 AM4/4/13
to
Enigma 1737 - Base jumping
New Scientist magazine, 23 February 2013.
By Peter Chamberlain.
In the country of Expluswye people do arithmetic
using a smaller base than our decimal system,
which uses base 10. My friend Basil recently
moved house in Expluswye and, when he sent me
his new address, commented that his new 3-digit
house number was a perfect square. To my eyes
Basil's house number is a prime, but when I
converted the number to decimal I saw that
Basil was right and that the number is indeed
a perfect square. This square written as a
decimal is a 3-digit number that shares no
digits with the house number as Basil writes it.
What is the number on Basil's new house?
Ciao,
Chappy.
New Scientist magazine, 23 February 2013.
By Peter Chamberlain.
In the country of Expluswye people do arithmetic
using a smaller base than our decimal system,
which uses base 10. My friend Basil recently
moved house in Expluswye and, when he sent me
his new address, commented that his new 3-digit
house number was a perfect square. To my eyes
Basil's house number is a prime, but when I
converted the number to decimal I saw that
Basil was right and that the number is indeed
a perfect square. This square written as a
decimal is a 3-digit number that shares no
digits with the house number as Basil writes it.
What is the number on Basil's new house?
Ciao,
Chappy.
Dave Baker
Apr 4, 2013, 5:30:21 AM4/4/13
to
"Chappy" <petergreg...@hotmail.com> wrote in message
news:37360303-4080-4bde...@googlegroups.com...
spreadsheet. Listing the 3 digit primes and converting them to decimal from
different starting bases the only one that results in a 3 digit perfect
square with no shared digits is the house number 647 in base 9 which
converts to 529 in decimal.
--
Dave Baker
Mark Brader
Apr 4, 2013, 6:50:20 AM4/4/13
to
Dave Baker:
> ...the only one that results in a 3 digit perfect square with no
on area 416, and 416 is 4 concatenated with 4^2, while 647 is 4^3
concatenated with 4^3/2 - 1, and 529 is one place off in one digit
from my previous area code before I moved to 416!
(Help... I'm turning into Don McDonald...)
--
Mark Brader | "Which humans of that time did here whether this place
Toronto | was cult place already at that time, extracts itself
m...@vex.net | from our knowledge." --from a web site for tourists
My text in this article is in the public domain.
> ...the only one that results in a 3 digit perfect square with no
> shared digits is the house number 647 in base 9 which converts
> to 529 in decimal.
And not only that, 647 was the first telephone area code overlaid
> to 529 in decimal.
on area 416, and 416 is 4 concatenated with 4^2, while 647 is 4^3
concatenated with 4^3/2 - 1, and 529 is one place off in one digit
from my previous area code before I moved to 416!
(Help... I'm turning into Don McDonald...)
--
Mark Brader | "Which humans of that time did here whether this place
Toronto | was cult place already at that time, extracts itself
m...@vex.net | from our knowledge." --from a web site for tourists
My text in this article is in the public domain.
Ted Schuerzinger
Apr 4, 2013, 7:26:13 AM4/4/13
to
On Thu, 4 Apr 2013 10:30:21 +0100, Dave Baker wrote:
> Maybe there's a clever way of doing this but it's a simple task using
> a spreadsheet. Listing the 3 digit primes and converting them to
> decimal from different starting bases the only one that results in a
> 3 digit perfect square with no shared digits is the house number 647
> in base 9 which converts to 529 in decimal.
I figured the simpler task would be to take the perfect squares and
> Maybe there's a clever way of doing this but it's a simple task using
> a spreadsheet. Listing the 3 digit primes and converting them to
> decimal from different starting bases the only one that results in a
> 3 digit perfect square with no shared digits is the house number 647
> in base 9 which converts to 529 in decimal.
convert *them* to the other bases, since there are fewer of those (17,
to be precise). I couldn't be bothered to do this when I saw somebody
had already responded.
--
Ted S.
fedya at hughes dot net
Now blogging at http://justacineast.blogspot.com
Dave Baker
Apr 4, 2013, 9:40:00 AM4/4/13
to
"Ted Schuerzinger" <fe...@hughes.spam> wrote in message
news:3in445sl...@justacineast.motzarella.org...
> On Thu, 4 Apr 2013 10:30:21 +0100, Dave Baker wrote:
>
>> Maybe there's a clever way of doing this but it's a simple task using
>> a spreadsheet. Listing the 3 digit primes and converting them to
>> decimal from different starting bases the only one that results in a
>> 3 digit perfect square with no shared digits is the house number 647
>> in base 9 which converts to 529 in decimal.
>
> I figured the simpler task would be to take the perfect squares and
> convert *them* to the other bases, since there are fewer of those (17,
> to be precise). I couldn't be bothered to do this when I saw somebody
> had already responded.
It's much easier to write the equations to convert a number from a lower
>
>> Maybe there's a clever way of doing this but it's a simple task using
>> a spreadsheet. Listing the 3 digit primes and converting them to
>> decimal from different starting bases the only one that results in a
>> 3 digit perfect square with no shared digits is the house number 647
>> in base 9 which converts to 529 in decimal.
>
> I figured the simpler task would be to take the perfect squares and
> convert *them* to the other bases, since there are fewer of those (17,
> to be precise). I couldn't be bothered to do this when I saw somebody
> had already responded.
base to a higher than vice versa unless you have a function already built in
to your spreadsheet which my old DOS thing doesn't. I never got the hang of
Excel. High to low involves division, remainders, more division, more
remainders etc etc. Low to high is just 1st digit x Base^2 + 2nd digit x
Base + 3rd digit.
--
Dave Baker
Puppet_Sock
Apr 4, 2013, 12:44:02 PM4/4/13
to
On Apr 4, 6:50 am, m...@vex.net (Mark Brader) wrote:
> Dave Baker:
>
> > ...the only one that results in a 3 digit perfect square with no
> > shared digits is the house number 647 in base 9 which converts
> > to 529 in decimal.
>
> And not only that, 647 was the first telephone area code overlaid
> on area 416, and 416 is 4 concatenated with 4^2, while 647 is 4^3
> concatenated with 4^3/2 - 1, and 529 is one place off in one digit
> from my previous area code before I moved to 416!
That would be 519, which was my area code as a kid.
> Dave Baker:
>
> > ...the only one that results in a 3 digit perfect square with no
> > shared digits is the house number 647 in base 9 which converts
> > to 529 in decimal.
>
> And not only that, 647 was the first telephone area code overlaid
> on area 416, and 416 is 4 concatenated with 4^2, while 647 is 4^3
> concatenated with 4^3/2 - 1, and 529 is one place off in one digit
> from my previous area code before I moved to 416!
Now I'm a 905-er.
> (Help... I'm turning into Don McDonald...)
Socks
Ted Schuerzinger
Apr 4, 2013, 3:50:57 PM4/4/13
to
On Thu, 4 Apr 2013 14:40:00 +0100, Dave Baker wrote:
>> I figured the simpler task would be to take the perfect squares and
>> convert *them* to the other bases, since there are fewer of those
>> (17, to be precise). I couldn't be bothered to do this when I saw
>> somebody had already responded.
>
> It's much easier to write the equations to convert a number from a
> lower base to a higher than vice versa unless you have a function
> already built in to your spreadsheet which my old DOS thing doesn't.
I would have done it by hand, not by spreadsheet.
>> I figured the simpler task would be to take the perfect squares and
>> convert *them* to the other bases, since there are fewer of those
>> (17, to be precise). I couldn't be bothered to do this when I saw
>> somebody had already responded.
>
> It's much easier to write the equations to convert a number from a
> lower base to a higher than vice versa unless you have a function
> already built in to your spreadsheet which my old DOS thing doesn't.
mbuck
Apr 8, 2013, 10:23:08 AM4/8/13
to fe...@hughes.net
On Friday, April 5, 2013 3:50:57 AM UTC+8, Ted Schuerzinger wrote:
> On Thu, 4 Apr 2013 14:40:00 +0100, Dave Baker wrote:
>
>
>
> >> I figured the simpler task would be to take the perfect squares and
>
> >> convert *them* to the other bases, since there are fewer of those
>
> >> (17, to be precise). I couldn't be bothered to do this when I saw
>
> >> somebody had already responded.
>
> >
>
> > It's much easier to write the equations to convert a number from a
>
> > lower base to a higher than vice versa unless you have a function
>
> > already built in to your spreadsheet which my old DOS thing doesn't.
>
>
>
> I would have done it by hand, not by spreadsheet.
>
>
I would have done it in the margin, but there wasn't enough room.
> On Thu, 4 Apr 2013 14:40:00 +0100, Dave Baker wrote:
>
>
>
> >> I figured the simpler task would be to take the perfect squares and
>
> >> convert *them* to the other bases, since there are fewer of those
>
> >> (17, to be precise). I couldn't be bothered to do this when I saw
>
> >> somebody had already responded.
>
> >
>
> > It's much easier to write the equations to convert a number from a
>
> > lower base to a higher than vice versa unless you have a function
>
> > already built in to your spreadsheet which my old DOS thing doesn't.
>
>
>
> I would have done it by hand, not by spreadsheet.
>
>
--riverman
Curlytop
Apr 13, 2013, 3:17:58 PM4/13/13
to
Mark Brader set the following eddies spiralling through the space-time
continuum:
> Dave Baker:
>> ...the only one that results in a 3 digit perfect square with no
>> shared digits is the house number 647 in base 9 which converts
>> to 529 in decimal.
>
> And not only that, 647 was the first telephone area code overlaid
> on area 416, and 416 is 4 concatenated with 4^2, while 647 is 4^3
> concatenated with 4^3/2 - 1, and 529 is one place off in one digit
> from my previous area code before I moved to 416!
>
> (Help... I'm turning into Don McDonald...)
In the book of Revelation, chapter 3^2 verse 4^2, you will find the largest
finite number in the Bible.
--
ξ: ) Proud to be curly
Interchange the alphabetic letter groups to reply
continuum:
> Dave Baker:
>> ...the only one that results in a 3 digit perfect square with no
>> shared digits is the house number 647 in base 9 which converts
>> to 529 in decimal.
>
> And not only that, 647 was the first telephone area code overlaid
> on area 416, and 416 is 4 concatenated with 4^2, while 647 is 4^3
> concatenated with 4^3/2 - 1, and 529 is one place off in one digit
> from my previous area code before I moved to 416!
>
> (Help... I'm turning into Don McDonald...)
finite number in the Bible.
--
ξ: ) Proud to be curly
Interchange the alphabetic letter groups to reply
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