..........contd..
9. In a crowded room, two people will probably share a birthday. Ok, so this is a bit vague. What does a "crowded room" mean and how probable is "probably". Very good questions!
It turns out and this can actually be seen very easily with some basic probability that if you have as little as 23 people in a room there will be a 50% chance that two of them have the same birthday.
I know this seems completely counter-intuitive. Allow me to add to that counter-intuitive feeling of yours, if the room grows to have 70 people present, you'll now have a 99.9% chance that two of them have the same birthday!
This is known as the birthday paradox (or the birthday problem) and I highly suggest you look further into this. I hope to write a short article about this problem very soon.
10. There is exactly 10 seconds in 6 weeks.
For those who are unaware, for any positive integer n, n! - read as "n factorial", represents the product of all positive integers less than or equal to n. S, for example, 5! = 5x4x3x2x1.
So, to see 10! seconds = 6 weeks, let's convert six weeks into seconds.
Let's now try to rewrite this so that it looks like 10!
11. The number of milliseconds in a day is equal to 5 to the power of 5 x 4 to the power of 4 x 3 to the power of 3 x 2 the power of 2 x 1 to the power of 1.
12. Multiplying ones will always give you palindromic numbers.
For those who are unaware, a palindromic number is simply a number that is the same backwards as forwards, for example 23432.
So, if you calculate 1x1, we get 1. Ok, that's a bit of a lazy palindrome, let's move on.
11 x 11 = 121,
111x111 = 12321
1111x1111 = 1234321 and keep going. If you multiply111111111 x 111111111 you get 12345678987654321.
Furthermore, it is not necessary to have the same number of ones in the two numbers you are multiplying. For example 11 x 1111 = 12221 and 111111 x 1111 = 123444321.
13. 18 is the only number that is twice the sum of its digits.
Although this is easily checked to be true for 18, it does require a little bit of thinking to argue that 18 is the only number for which this is true.
14. The number 0.9999.....is exactly equal to 1.
I can give a rather simple proof of this.
Let x = 0.9999.....
Then, multiplying both sides of the equation by 10, we have
10 x 9.9999....
If we now subtract x = 0.9999 from both sides we have
10x - x = (9.9999.....) - (0.9999)
* 9x = 9
x = 1.
A similar fact holds for any number containing an infinite string of 9s.
For example 0.4999.....= 0.5, 19.999...= 20 and -2.999....= -3.
If I'm honest, I'm never fully happy with this proof. It certainly serves its purpose to highlight what is going on but, for those who have studied any level of real analysis, you may feel like this is a cheap trick. I somewhat agree and for those who are interested you should look up how to prove this fact by using limits of sequences!
So, that's it, 14 interesting math facts to make you the life of any party.
......concluded.
Tailpiece.
Got up at 5, the chores and was ready by a half past 7. Sajish had dropped by, on the dot, at a half past 7. We took off for Kochi and dropped Lekha at Shenoy Care by 10 o'clock and then, headed for the Diabetic Care of India at Panampilli Nagar.
Satish Bhat and I remembered Ramakrishnan, I told him about my recent observations and another medicine has been added to the ones that I'm having.
Padmanabha Shenoy was happy with Lekha's progress and he has given the clearance for the dental implants and allied work.
We returned home by a half past 4 but not before having our lunch of packed idlis by the wayside shade past Idappalli.
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