Teaser 2512
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Cactus
Nov 14, 2010, 2:27:51 AM11/14/10
to Sunday Times Teaser Solutions
Sunday Times Teaser 2512 by Graham Smithers
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I have written down a three number numbers and two four digit numbers
that, between them, use all the digits 0 to 9 exactly once. One of
them is a perfect square, one a perfect cube and one a prime. If you
knew which of the square, the cube and the prime was the smallest, you
could then work out what the three numbers are. What are they?
Cactus
----------------------------------------------------------------------
I have written down a three number numbers and two four digit numbers
that, between them, use all the digits 0 to 9 exactly once. One of
them is a perfect square, one a perfect cube and one a prime. If you
knew which of the square, the cube and the prime was the smallest, you
could then work out what the three numbers are. What are they?
Cactus
Cactus
Nov 14, 2010, 2:36:12 AM11/14/10
to Sunday Times Teaser Solutions
Using all the digits 0 to 9 exactly once, I have written down a three
digit number and two four digit numbers.
One of them is a perfect square, one a perfect cube and one a prime.
If you knew which of the square, the cube and the prime was the
What are they?
Peter
Nov 14, 2010, 3:19:12 AM11/14/10
to Sunday Times Teaser Solutions
Good Morning All,
I looked into the Sunday Times site. Obviously, two 3-digit numbers
and one 4-digit number
are to be found using 10 different digits.
It was a straightforward but somewhat tedious task to find compatible
sets of squares, cubes and primes. I found 18 different sets, allowing
possible permutations of digits within some numbers (such as 125,
512).
A unique set is obtained if I knew that the smallest number is a
square.
Peter
I looked into the Sunday Times site. Obviously, two 3-digit numbers
and one 4-digit number
are to be found using 10 different digits.
It was a straightforward but somewhat tedious task to find compatible
sets of squares, cubes and primes. I found 18 different sets, allowing
possible permutations of digits within some numbers (such as 125,
512).
A unique set is obtained if I knew that the smallest number is a
square.
Peter
Cactus
Nov 14, 2010, 4:23:03 AM11/14/10
to Sunday Times Teaser Solutions
mistake:
-----------------------------------------------------------------------
Using all the digits 0 to 9 exactly once, I have written down two
three
digit numbers and a four digit number.
One of them is a perfect square, one a perfect cube and one a prime.
If you knew which of the square, the cube and the prime was the
smallest, you could then work out what the numbers are.
What are they?
text on the site at:
https://sites.google.com/site/sundaytimesteasers/
where I can easily edit it.
Cactus
Guy
Nov 14, 2010, 7:10:52 AM11/14/10
to Sunday Times Teaser Solutions
Greetings all,
I think this is the complete list of eligible [perfect cubes, perfect
squares, primes]. In order to find unique solution you must know that
the perfect square is the smallest.
125 6084 379
125 6084 397
125 6084 739
125 6084 937
125 8649 307
216 784 5039
216 784 5309
216 784 5903
512 6084 379
512 6084 397
512 6084 739
512 6084 937
512 8649 307
729 841 6053
729 5041 683
729 5041 863
6859 324 107
6859 324 701 *
9261 784 503
Brian: thanks for setting up the new website.
I think this is the complete list of eligible [perfect cubes, perfect
squares, primes]. In order to find unique solution you must know that
the perfect square is the smallest.
125 6084 379
125 6084 397
125 6084 739
125 6084 937
125 8649 307
216 784 5039
216 784 5309
216 784 5903
512 6084 379
512 6084 397
512 6084 739
512 6084 937
512 8649 307
729 841 6053
729 5041 683
729 5041 863
6859 324 107
6859 324 701 *
9261 784 503
Brian: thanks for setting up the new website.
Peter
Nov 14, 2010, 7:51:26 AM11/14/10
to Sunday Times Teaser Solutions
Hello Guy,
using tables of squares, cubes and primes I produced the same list.
But I miscounted 18 instead of 19 sets because my "list" was
distributed in a number of smaller tables of S,C,P.
Peter
using tables of squares, cubes and primes I produced the same list.
But I miscounted 18 instead of 19 sets because my "list" was
distributed in a number of smaller tables of S,C,P.
Peter
Garry
Nov 14, 2010, 8:48:30 AM11/14/10
to Sunday Times Teaser Solutions
Hello Brian
Re. the new site, will all members of this group be able to add
comments about each teaser, i.e. conduct things rather like we do now?
Or will discussion continue here, with the new site being used just
for reference?
Garry
Re. the new site, will all members of this group be able to add
comments about each teaser, i.e. conduct things rather like we do now?
Or will discussion continue here, with the new site being used just
for reference?
Garry
Teasemaster
Nov 14, 2010, 9:09:37 AM11/14/10
to Sunday Times Teaser Solutions
This will amuse everyone!
http://www.theanswerbank.co.uk/Quizzes-and-Puzzles/Riddles/Question928129.html
"Yesterday I was so annoyed with this teaser that I searched for
'Teaser 2499' and, lo and behold, found a site where a group of very
bright types were discussing the problem!"
Our fame spreads abroad!
T2512
Peter is right about "tedious" but I shortened the task.
a. Observe that of the squares <1000 and the cubes <10000 only one
contains a 0 (4096=16^3)
Exploring that option gives no possible 3-digit square. Thus, the
prime contains a 0.
b. Likely the answer will be hidden in squares, cubes or 0-containing
primes with anagrammatic digits - (squares) = (169,196,961),(256,625);
(cubes) = (125,512); (primes) = (107,701),(709,907)
c. Assuming the square is the smallest (for the moment) we need to
find a higher and a lower cube, or a higher and a lower prime. That
only gives (Sq,Cu,Pr) = (324,6859,107/701) and knowing Sq is lowest
gives (324,6859,701)
d. The same analysis starting with the assumption of Cu lowets and Pr
lowest produces no result.
324 6859 701
http://www.theanswerbank.co.uk/Quizzes-and-Puzzles/Riddles/Question928129.html
"Yesterday I was so annoyed with this teaser that I searched for
'Teaser 2499' and, lo and behold, found a site where a group of very
bright types were discussing the problem!"
Our fame spreads abroad!
T2512
Peter is right about "tedious" but I shortened the task.
a. Observe that of the squares <1000 and the cubes <10000 only one
contains a 0 (4096=16^3)
Exploring that option gives no possible 3-digit square. Thus, the
prime contains a 0.
b. Likely the answer will be hidden in squares, cubes or 0-containing
primes with anagrammatic digits - (squares) = (169,196,961),(256,625);
(cubes) = (125,512); (primes) = (107,701),(709,907)
c. Assuming the square is the smallest (for the moment) we need to
find a higher and a lower cube, or a higher and a lower prime. That
only gives (Sq,Cu,Pr) = (324,6859,107/701) and knowing Sq is lowest
gives (324,6859,701)
d. The same analysis starting with the assumption of Cu lowets and Pr
lowest produces no result.
324 6859 701
Cactus
Nov 14, 2010, 9:43:15 AM11/14/10
to Sunday Times Teaser Solutions
Hi Garry,
It's a good question. The google site software is vey easy to use but
the google group software allows much better control over
participants. As a result of the latter I have been able to prevent
our group being spammed whereas other forums have been ruined by
spamming. And, sadly, if I allow web site commenting, everyone who is
allowed to comment is also allowed to do literally any editing of the
whole site (how stupid is that).
Right now everyone who is a member of this teaser group should also be
able to add comments on the web and I would like people to try this to
see if it serves our purpose. Since the comments will be linked to
each teaser, this seems to me to be better than our current approach.
Hence if people like it, I would personally prefer to move commenting
over to the web site.
I would then only keep this discussion group to provide good control
over our users since, if anyone tries to interfere with the web site,
all I have to do is to remove them from the discussion group (I have
set it up so that only members of this group can comment on and edit
the web site).
But I would like to hear what others think. For teaser text, however,
I will now use the web site because I often find I need to edit the
text as I do the teasers and find that my description is wrong.
Brian
It's a good question. The google site software is vey easy to use but
the google group software allows much better control over
participants. As a result of the latter I have been able to prevent
our group being spammed whereas other forums have been ruined by
spamming. And, sadly, if I allow web site commenting, everyone who is
allowed to comment is also allowed to do literally any editing of the
whole site (how stupid is that).
Right now everyone who is a member of this teaser group should also be
able to add comments on the web and I would like people to try this to
see if it serves our purpose. Since the comments will be linked to
each teaser, this seems to me to be better than our current approach.
Hence if people like it, I would personally prefer to move commenting
over to the web site.
I would then only keep this discussion group to provide good control
over our users since, if anyone tries to interfere with the web site,
all I have to do is to remove them from the discussion group (I have
set it up so that only members of this group can comment on and edit
the web site).
But I would like to hear what others think. For teaser text, however,
I will now use the web site because I often find I need to edit the
text as I do the teasers and find that my description is wrong.
Brian
Garry
Nov 14, 2010, 11:59:23 AM11/14/10
to Sunday Times Teaser Solutions
Hello Brian
With all of the maths reference material on the site, it would seem a
good idea to use it exclusively, but the possibility of vandalism
could be a snag. Presumably there'd always be an archive to restore
the material if that occurred? You say that "we should be able to add
comments", does this mean that it would be desirable, or that we can
in fact do so - and if so, how?
Garry
With all of the maths reference material on the site, it would seem a
good idea to use it exclusively, but the possibility of vandalism
could be a snag. Presumably there'd always be an archive to restore
the material if that occurred? You say that "we should be able to add
comments", does this mean that it would be desirable, or that we can
in fact do so - and if so, how?
Garry
Cactus
Nov 14, 2010, 3:21:50 PM11/14/10
to Sunday Times Teaser Solutions
To enable comments you have to be signed in to your gmail account.
Once you sign in the pages should have a comment line added, which you
can use to post comments.
Brian
Teasemaster
Nov 14, 2010, 8:53:48 PM11/14/10
to Sunday Times Teaser Solutions
Personally, I find the level of personal information required for a
gmail account to be intrusive. I value my privacy, and I won't be data-
mined. Anyone else, or just me?
TM
gmail account to be intrusive. I value my privacy, and I won't be data-
mined. Anyone else, or just me?
TM
Garry
Nov 15, 2010, 6:45:34 AM11/15/10
to Sunday Times Teaser Solutions
Hi Brian
I've gone to the site, when signed up to gmail, but apparently without
being able to add anything. I'm guessing, being technologically
challenged, that this is because I'm a member of this group only via
my Yahoo mail account, because you don't know my gmail account. If
this is so, please note that the latter is x...@gmail.com, where xxx is
exactly the same as what precedes @yahoo.co.uk, and enrol me
accordingly.
Garry
I've gone to the site, when signed up to gmail, but apparently without
being able to add anything. I'm guessing, being technologically
challenged, that this is because I'm a member of this group only via
my Yahoo mail account, because you don't know my gmail account. If
this is so, please note that the latter is x...@gmail.com, where xxx is
exactly the same as what precedes @yahoo.co.uk, and enrol me
accordingly.
Garry
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