Counting - discussion thread

[RobbieM]

It'll be interesting when we get past the current year and can't rely on historical events any more...

But it'll be interesting to list 'predictions' (political/ecological etc.) about future years, and later on we can see if they come true...!

[RobbieM]

Sometimes this game leaves me longing to visit parts of the country I've never been to. Like Lichfield in Staffordshire, where I could sample the delights of 1709 The Brasserie:

Just over the road from 'The Crown' pub, where I had a meal in January. It was on the pub's TV screen that I saw the breaking news of the sad events at the Charlie offices in Paris...

[DrainBrain]

...

1729 = 1^3 + 12^3 = 9^3 + 10^3

• And that's also what I think I'd've written had it been me who did 1729!

And me. Definitely.

[RobbieM]

Okay, I've done 1734, and I will now say my farewells for a few weeks! Off on holiday, so I won't be accessing the Forum at all.

I trust you all to do the business, and keep going towards the 2000 mark!

Cheers,
RobbieM

[GuyBarry]

Okay, I've done 1734, and I will now say my farewells for a few weeks! Off on holiday, so I won't be accessing the Forum at all.

I trust you all to do the business, and keep going towards the 2000 mark!

Thanks for all your help! I'm keeping an eye on QI and we're going much faster than them, so fingers crossed...

[GuyBarry]

This time last week, QI were on 1842 and we were on 1700. As I write this, QI are on 1852 and we're on 1748.

So they've gained 10 while we've gained 48. At this rate, we'll have overtaken them in less than three weeks' time - much sooner than I thought, around the 1880 mark. Since RobbieM is out of action for a few weeks it may take a little longer, but I reckon we can easily beat them to 2000 as long as we maintain the pace. Keep going everyone!

[GuyBarry]

As I predicted, things have slowed down somewhat this week, but we're still on course to overtake QI before 2000. This time last week, they were on 1852 and we were on 1748; as I write this, they're on 1861 and we're on 1766, which means they've gained 9 to our 18. Extrapolating, we should pass them around 1956 in about ten-and-a-half weeks' time (the middle of September). Good work everyone!

[GuyBarry]

Weekly progress report: I'm pleased to say we're gaining ground! Since this time last week, QI have advanced by 14 to 1875, but we've advanced by 32 to 1798. This gives us a mere 77 to catch up, which at the current rate we should do in 30 days (around the 1935 mark). Then it should take us only a further two weeks to reach the magic 2000 - around August 24th by my calculations. Keep it up folks...

[GuyBarry]

[Post now corrected as indicated]

Just to show I don't believe everything I read on the internet but probably should: "1819 has a 7th power that contains the same digits as 322^9" (from What's Special About This Number?):

1819^7 = 65891424018613967932339
322^9 = 37213699403613156884992

[DrainBrain]

Just to show I don't believe everything I read on the internet: "1819 has a 7th power that contains the same digits as 322^9" (from What's Special About This Number?):

1819^7 = 65891424018613967932339
322^9 = 37213699403616156884992

Almost, but the top number has four 3's and three 6's, whereas the bottom number has four 6's and three 3's. Bad luck.

Um, you have a typo in the digits of 322^9. Guess which digit got changed!

[GuyBarry]

Oops! That's a shame - I really wanted to use that fact. Thanks.

[DrainBrain]

Well you've effectively used it here. It is an extraordinary fact.

I wonder how common such things are.

Edit to partially answer my own question:
There are only 3107 powers of numbers less than 10000 that have exactly 23 decimal digits, which suggests that a digit collision such as this is a huge coincidence.

[GuyBarry]

Well you've effectively used it here. It is an extraordinary fact.

I've corrected it now.

I wonder how common such things are.

I wonder how anyone ever finds such things out! It's not the sort of thing you're likely to go looking for...

[DrainBrain]

I wonder how anyone ever finds such things out! It's not the sort of thing you're likely to go looking for...

Mathematicians look at all sorts of weird stuff: http://oeis.org/search?q=anagram

Also, I've added an edit to my post above.

[DrainBrain]

All instances where the base number is less than 10000, with length 23 digits:

5554^6 = 29351834668648900703296
5585^6 = 30348628169708496390625

4969^6 = 15052685242962387973681
6785^6 = 97566137438122528890625

322^9 = 37213699403613156884992
1819^7 = 65891424018613967932339

6067^6 = 49870528386460302234169
6568^6 = 80278428935009316634624

5621^6 = 31541439632080693959721
746^8 = 95920320184934913761536

5936^6 = 43748518799030653812736
6769^6 = 96193800735536743742881

4672^6 = 10399608842827495112704
5188^6 = 19498437219006281027584

5583^6 = 30283479081708435342369
1914^7 = 94100847338933725682304

4854^6 = 13079725568982661202496
6366^6 = 66557929860730142922816

Extending the search to numbers less than 1000000 gives oodles and oodles of possibilities.

I hope I didn't mess up the copy-pasting.