## Buffon’s puzzling numbers

In a book about the celebrated French naturalist Georges-Louis Leclerc, Comte de Buffon (best known to mathematicians for his needle), I found the following picture, apparently without explanation (unless I missed something):

Apologies for the poor quality of the picture. Round the edge of the cards are beautiful illustrations of birds and fish, similar to those in his famous work Histoire Naturelle.

But what do the numbers mean? If they are not clear from the picture, here they are by rows: 24, 6, 1; 44, 14, 25; 53, 39, 49; 66, 58, 69; 86, 79, 70. The numbers 24, 1, 39, 86, 70 in the four corners and the centre are on shaded backgrounds.

Was Buffon a secret lotto player, who amused himself by illustrating the lotto cards?

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## About Peter Cameron

I count all the things that need to be counted.
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### 10 Responses to Buffon’s puzzling numbers

• 1,6,14,24 gives several hits but adding 25 kills them all, Similarly, 24,6,1 gives several hits but adding 44 leaves none. Did you try Superseeker?

1. Cristina says:

Here is one observation. Think of the array as a planar graph with edges between any two numbers that “touch”. Label the edges as the absolute value of the difference between the incident vertices. Then any triangle is degenerate in the sense that the sum of the weights of two of the edges is the weight of the third. I haven’t thought about what this means. I know this is cumbersome but I can’t see anything else.

• Cristina says:

The graph is not planar. Sorry.

• Cristina says:

Well… that observation doesn’t help because it is trivially true for any array of numbers.

• Maybe they are just random numbers …

2. Chris Jefferson says:

After trying some maths. I tried googling for the numbers, and this website contains a bingo card with exactly these numbers.. seems unlikely to be a coincidence (because that webpage is the only one which contains “24 44 53 66 86”), but I can’t find any rhyme or reason as to how those cards were created.

http://www.jeugdwerker.be/downloads/team-bingo-formulieren.pdf

The middle row finds this quote from a book, which could well be a coincidence, and I cannot find the rest of the book to see the wider context unfortunately.

3. Thanks, Chris — that was my original guess. Was Buffon so serious about lotto that he devoted time to produce those detailed illustrations, or has someone just lifted them from his book for decoration? Who knows?

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