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Check out Mark Dominus's great blog. Link to follow-on post at end of this one.
https://blog.plover.com/math/irish-lo...

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Paper on other method to get Ludgates's values: https://treasures.scss.tcd.ie/miscell...

All of the numbers I found are below. So many numbers. Presented three different ways, which is really unhelpful.

Huge thanks to my Patreon supporters. They put the teeth on my cogs.   / standupmaths  

CORRECTIONS
- Yes, the invention of logs in 1614 is 410 years ago, not 400, as I said around 06:10. On the fly my brain confused it with the 1624 publishing of Arithmetica Logarithmica, the first great log table book. First noted by AlexSh789.
- In the completed table around 11:54 I accidentally put in some products where are not the result of two one-digit numbers (60, 80 and 90), and thus are not needed. First pointed out by Frederico via email.
- Let me know if you spot anything else!

Filming and editing by Alex Genn-Bash
Written and performed by Matt Parker
Produced by Nicole Jacobus
Cogputer build by Lisa Mather and Katie Steckles
Tree build by Nina, Carrie and assisted by Laura.
Extra material by Adam Atkinson
Music by Howard Carter
Design by Simon Wright and Adam Robinson

MATT PARKER: Stand-up Mathematician
Website: http://standupmaths.com/
US book: https://www.penguinrandomhouse.com/bo...
UK book: https://mathsgear.co.uk/collections/b...


0-9 COGPUTER

0 cog: 1 teeth
1 cog: 42 teeth
2 cog: 41 teeth
3 cog: 27 teeth
4 cog: 40 teeth
5 cog: 8 teeth
6 cog: 26 teeth
7 cog: 18 teeth
8 cog: 39 teeth
9 cog: 12 teeth

LABELS ON MIDDLE COG:

CE, --, 00, --, --, --, --, --, --, 00, --, --, --, 00, --, --, 25, --, --, 00, 45, --, --, --, 81, --, 35, 00, 00, --, 63, --, --, --, 30, 15, 49, --, 54, 27, 00, 00, 00, 00, 42, 21, --, 40, 20, 10, 05, 72, 36, 18, 09, --, --, 56, 28, 14, 07, --, --, --, --, 48, 24, 12, 06, 03, --, --, --, --, --, --, --, --, 64, 32, 16, 08, 04, 02, 01

1-9 CHRISTMAS TREE

Present 1 is 7 units tall
Present 2 is 5 units tall
Present 3 is 18 units tall
Present 4 is 3 units tall
Present 5 is 21 units tall
Present 6 is 16 units tall
Present 7 is 28 units tall
Present 8 is 1 units tall
Present 9 is 29 units tall

Bauble 1 is 14 units high
Bauble 2 is 12 units high
Bauble 3 is 25 units high
Bauble 4 is 10 units high
Bauble 5 is 28 units high
Bauble 6 is 23 units high
Bauble 7 is 35 units high
Bauble 8 is 8 units high
Bauble 9 is 36 units high
Bauble 10 is 26 units high
Bauble 12 is 21 units high
Bauble 14 is 33 units high
Bauble 15 is 39 units high
Bauble 16 is 6 units high
Bauble 18 is 34 units high
Bauble 20 is 24 units high
Bauble 21 is 46 units high
Bauble 24 is 19 units high
Bauble 25 is 42 units high
Bauble 27 is 47 units high
Bauble 28 is 31 units high
Bauble 30 is 37 units high
Bauble 32 is 4 units high
Bauble 35 is 49 units high
Bauble 36 is 32 units high
Bauble 40 is 22 units high
Bauble 42 is 44 units high
Bauble 45 is 50 units high
Bauble 48 is 17 units high
Bauble 49 is 56 units high
Bauble 54 is 45 units high
Bauble 56 is 29 units high
Bauble 63 is 57 units high
Bauble 64 is 2 units high
Bauble 72 is 30 units high
Bauble 81 is 58 units high

2-9 CHRISTMAS TREE CARD

2: 3
3: 12
4: 2
5: 17
6: 11
7: 24
8: 1
9: 20

height: bauble number
2: 64
3: 32
4: 16
5: 8
6: 4
12: 48
13: 24
14: 12
15: 6
18: 40
19: 20
20: 10
21: 72
22: 36
23: 18
24: 9
25: 56
26: 28
27: 14
28: 30
29: 15
31: 54
32: 27
34: 25
35: 42
36: 21
37: 45
40: 81
41: 35
44: 63
48: 49

THE END

PS https://forms.gle/UqZQRwYe26SLJjMn8