21322314 is a number that gives its own inventory.
It has 2 1s, 3 2s, 2 3s, 1 4.
It tallies each numeral.
Other examples are 22 and 1022
How many numbers describe themselves, in this way
Rule: the “numerals” have to be listed in increasing order so you can’t just obtain fresh examples by reordering, eg 14322123.
dv said:
Rule: the “numerals” have to be listed in increasing order so you can’t just obtain fresh examples by reordering, eg 14322123.
Aight.
Rule 303 said:
dv said:Rule: the “numerals” have to be listed in increasing order so you can’t just obtain fresh examples by reordering, eg 14322123.
Aight.
It is spelt eight
1022
20022
300022
4000022
50000022
600000022
7000000022
80000000022
900000000022
Ok, that’s the zeros done :)
sibeen said:
1022
20022
300022
4000022
50000022
600000022
7000000022
80000000022
900000000022Ok, that’s the zeros done :)
So you’re saying that 300022 has three 0s, and zero 0s, and two 2s. This is wrong because you neglected to tally the 3s (there is one 3) and also because there aren’t zero 0s.
All of these are wrong for similar reasons.
dv said:
Rule 303 said:
dv said:Rule: the “numerals” have to be listed in increasing order so you can’t just obtain fresh examples by reordering, eg 14322123.
Aight.
It is spelt eight
Nyet.
Of course this makes me a dumb cnut for including 1022. It would be appropriate for you to shame me about that for 36 hours. Can’t even edit the OP. Fuck me literally dead.
So there are only two examples I’ve given. 22 and 21322314.
dv said:
Of course this makes me a dumb cnut for including 1022. It would be appropriate for you to shame me about that for 36 hours. Can’t even edit the OP. Fuck me literally dead.So there are only two examples I’ve given. 22 and 21322314.
Ahh, that makes me feel a bit better. I was going to pull you on the 1022, then thought about it and went this is what you must mean.
The 36 hours, does the clock have to start now? It’s just that I probably have to go out for a few hours this afternoon.
21322315
21322316
21322317
21322318
21322319
Bubblecar said:
21322315
21322316
21322317
21322318
21322319
Nice.
And equivalently, 10213223
dv said:
Of course this makes me a dumb cnut for including 1022. It would be appropriate for you to shame me about that for 36 hours. Can’t even edit the OP. Fuck me literally dead.So there are only two examples I’ve given. 22 and 21322314.
So nothing with a zero in it then?
chips in the pan
sizzling sounds
party_pants said:
dv said:
Of course this makes me a dumb cnut for including 1022. It would be appropriate for you to shame me about that for 36 hours. Can’t even edit the OP. Fuck me literally dead.So there are only two examples I’ve given. 22 and 21322314.
So nothing with a zero in it then?
21322310
Bubblecar said:
party_pants said:
dv said:
Of course this makes me a dumb cnut for including 1022. It would be appropriate for you to shame me about that for 36 hours. Can’t even edit the OP. Fuck me literally dead.So there are only two examples I’ve given. 22 and 21322314.
So nothing with a zero in it then?
21322310
But it has to be ascending, so dv’s example:
10213223
…is the correct arrangement.
Bubblecar said:
Bubblecar said:
party_pants said:So nothing with a zero in it then?
21322310
But it has to be ascending, so dv’s example:
10213223
…is the correct arrangement.
A finite number of solutions, because there can be no more than 20 digits.
There can be at most one zero, at most one 9, 8, 7, 6.
Can there be two fives, i don’t think so.
Thinking that way could narrow down the total number of solutions.
party_pants said:
dv said:
Of course this makes me a dumb cnut for including 1022. It would be appropriate for you to shame me about that for 36 hours. Can’t even edit the OP. Fuck me literally dead.So there are only two examples I’ve given. 22 and 21322314.
So nothing with a zero in it then?
There can be exactly one 0, in the 2nd position, and if it is there, then the number in the first position has to be 1.
I realise now that this is not a very entertaining puzzle as it basically would involve unrewarding but straightforward labour. You could start by observing that the “tallies” have to be selected from the “numerals”. e.g. you know that 311617 isn’t a member without even checking, because there’s a 3 in the tallies but no 3 in the numerals. You would also know that the higher numerals have to have 1 as the tally. e.g. if “29” appeared it would mean that one of the tallies must be 9: not likely, since at the very most all the tallies have to add to 20.
I’ll let you know now that there are 99 such numbers.
Some fun facts:
Obviously, the number of digits in these numbers has to be even. There is exactly one 2 digit number, but there are no 4 digit, 6 digit, or 12 digit numbers in the list.
So I’ll cut down this so-called puzzle to two simple requirements:
a) give a short proof that there are no 4 digit numbers of this type.
b) there is exactly one 20 digit number in the list. What is it?
I’ll present below the first 98.
22
10213223
10311233
10313314
10313315
10313316
10313317
10313318
10313319
21322314
31123314
21322315
31123315
21322316
31123316
21322317
31123317
21322318
31123318
21322319
31123319
31331415
31331416
31331417
31331418
31331419
31331516
31331517
31331518
31331519
31331617
31331618
31331619
31331718
31331719
31331819
1031223314
1031223315
1031223316
1031223317
1031223318
1031223319
3122331415
3122331416
3122331417
3122331418
3122331419
3122331516
3122331517
3122331518
3122331519
3122331617
3122331618
3122331619
3122331718
3122331719
3122331819
10413223241516
10413223241517
10413223241518
10413223241519
10413223241617
10413223241618
10413223241619
10413223241718
10413223241719
10413223241819
41322324151617
41322324151618
41322324151619
41322324151718
41322324151719
41322324151819
41322324161718
41322324161719
41322324161819
41322324171819
1051322314251617
1051322314251618
1051322314251619
1051322314251718
1051322314251719
1051322314251819
1051322325161718
1051322325161719
1051322325161819
1051322325171819
5132231425161718
5132231425161719
5132231425161819
5132231425171819
5132232516171819
106132231415261718
106132231415261719
106132231415261819
106132231426171819
106132231526171819
613223141526171819
Yeah I lost interest pretty quickly :)
Bubblecar said:
Yeah I lost interest pretty quickly :)
Who’s susceptible to nerdsniping here?
dv said:
Bubblecar said:
Yeah I lost interest pretty quickly :)
Who’s susceptible to nerdsniping here?
I doubt there are any real tragics on board these days, apart from possibly your good self.
Bubblecar said:
dv said:
Bubblecar said:
Yeah I lost interest pretty quickly :)
Who’s susceptible to nerdsniping here?
I doubt there are any real tragics on board these days, apart from possibly your good self.
SAD
10713223141516271819
sibeen said:
10713223141516271819
:)
I reckon that would’ve taken me a few more minutes.
I was about halfway there.
:)
sibeen said:
10713223141516271819
Well ding my dongs but that was speedy. Well done.
dv said:
sibeen said:
10713223141516271819
Well ding my dongs but that was speedy. Well done.
He probably used a Babbage Engine.
Bubblecar said:
dv said:
sibeen said:
10713223141516271819
Well ding my dongs but that was speedy. Well done.
He probably used a Babbage Engine.
From the Bolour supplement
Okay smartballs sibeen, what about the other part of the challenge
a) give a short proof that there are no 4 digit numbers of this type.
dv said:
Okay smartballs sibeen, what about the other part of the challengea) give a short proof that there are no 4 digit numbers of this type.
Because 22 is the only two number combination that works in isolation.
1
party_pants said:
1
Doesn’t fit the format.
I sent this puzzle to fivethirtyeight and they published it, so that’s nice.
https://fivethirtyeight.com/features/how-many-numbers-contain-the-numbers-of-their-numbers/
dv said:
I sent this puzzle to fivethirtyeight and they published it, so that’s nice.
Hopefully they will be better than us at coming up with answers.
dv said:
I sent this puzzle to fivethirtyeight and they published it, so that’s nice.https://fivethirtyeight.com/features/how-many-numbers-contain-the-numbers-of-their-numbers/
Rushes over to fivethirtyeight to answer.
dv said:
I sent this puzzle to fivethirtyeight and they published it, so that’s nice.https://fivethirtyeight.com/features/how-many-numbers-contain-the-numbers-of-their-numbers/
Don’t forget us little folk now that you’re famous.
dv said:
I sent this puzzle to fivethirtyeight and they published it, so that’s nice.https://fivethirtyeight.com/features/how-many-numbers-contain-the-numbers-of-their-numbers/
Well done.
https://amp.brisbanetimes.com.au/national/worst-ever-immigration-minister-asylum-seekers-jet-in-under-dutton-s-nose-20190302-p511d8.html
ChrispenEvan said:
https://amp.brisbanetimes.com.au/national/worst-ever-immigration-minister-asylum-seekers-jet-in-under-dutton-s-nose-20190302-p511d8.html
although it kinda fits being about numbers it is still a wrong thread post.
ChrispenEvan said:
https://amp.brisbanetimes.com.au/national/worst-ever-immigration-minister-asylum-seekers-jet-in-under-dutton-s-nose-20190302-p511d8.html
Well, that was scathing (but rightly deserved).
Michael V said:
ChrispenEvan said:
https://amp.brisbanetimes.com.au/national/worst-ever-immigration-minister-asylum-seekers-jet-in-under-dutton-s-nose-20190302-p511d8.html
Well, that was scathing (but rightly deserved).
‘“This has the very real risk to Australia of creating a large and growing number of failed asylum seekers in our community, just like in Europe and the US. These vulnerable people will become a permanently exploited underclass in Australia. And what do we hear from Dutton and Morrison on this actual risk? Crickets!’‘
Or, in L/NP terms ‘a supply of labour who are too scared to even join a union, much less complain about the slavery-like conditions of their employment – just what WorkChoices never quite delivered’.
We have controversy. 538 is now telling us that there is 109 of these numbers.
https://fivethirtyeight.com/features/get-perplexed-with-some-games-of-hex/
I demand a ruling!
1011112131415161718
1011112131415161719
1011112131415161819
1011112131415171819
1011112131416171819
1011112131516171819
1011112141516171819
1011113141516171819
1111213141516171819
101112213141516171819
These are the additional numbers, so the last one is:
One zero, eleven ones, two twos, one three, one four ……
sibeen said:
We have controversy. 538 is now telling us that there is 109 of these numbers.https://fivethirtyeight.com/features/get-perplexed-with-some-games-of-hex/
I demand a ruling!
Remind me, please: what was the agreed number of numbers before the puzzle was submitted for publication?
Michael V said:
sibeen said:
We have controversy. 538 is now telling us that there is 109 of these numbers.https://fivethirtyeight.com/features/get-perplexed-with-some-games-of-hex/
I demand a ruling!
Remind me, please: what was the agreed number of numbers before the puzzle was submitted for publication?
deevs came up with 99.
sibeen said:
10111121314151617181011112131415161719
1011112131415161819
1011112131415171819
1011112131416171819
1011112131516171819
1011112141516171819
1011113141516171819
1111213141516171819
101112213141516171819
These are the additional numbers, so the last one is:
One zero, eleven ones, two twos, one three, one four ……
Seems a new rule has been introduced, that destroys the puzzle.
Deevs, a few new posts and some controversy.
The editor did not pose the question in quite the same way that I did, and its a crucial difference.