@johncarlosbaez@mathstodon.xyz
2025-12-16 19:52 UTC
@alisonkiddle@mathstodon.xyz -
The chances are 1/2¹⁰ and 1/6⁴, respectively. I know 2¹⁰ = 1024, but what's 6⁴? I have a vague memory that it's 1296, but let me think. It's 36 squared. I guess just multiply it out in my mind. 6 times 6 is 36, 6 times 30 is 180, 30 times 30 is 900, 900 + 180 + 180 + 36 = 1080 + 180 + 36 = 1260 + 36 = 1296. Okay, good. So it's more likely to roll 10 heads than to roll four 6's.
I'm worrying about 6³ and worked out that it's 216. Sounds very familiar. I used to know these numbers better! I like powers of numbers and feel happy knowing a bunch of them. They have a nice feeling to them.
Replies (2)
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@BartoszMilewski@mathstodon.xyz 2025-12-16 20:36
@johncarlosbaez@mathstodon.xyz @alisonkiddle@mathstodon.xyz I whould divide the two numbers and see if the result is less than one. The advantage is that you can cancel the factor of 2⁴
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@alisonkiddle@mathstodon.xyz 2025-12-16 21:14
@johncarlosbaez@mathstodon.xyz I also have numbers who feel like old friends. I'm glad I could reacquaint you with one of yours