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Science & Mathematics Anything else you have noticed ?

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There's a whole bunch of these.

11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
etc.
When I was in high school many years ago I noticed that you could tell if a number was divisible by eleven (in particular in the hundreds) if the first and last number added up to equal the middle number, also the two outside numbers were the multiplier. E.g 143 = 13x11, 264 = 24x11, 781 = 71x11. I haven't checked these so I am going to look pretty stupid if I'm wrong. But I am almost positive they will all be right.
 
When I was in high school many years ago I noticed that you could tell if a number was divisible by eleven (in particular in the hundreds) if the first and last number added up to equal the middle number, also the two outside numbers were the multiplier. E.g 143 = 13x11, 264 = 24x11, 781 = 71x11. I haven't checked these so I am going to look pretty stupid if I'm wrong. But I am almost positive they will all be right.

good get. and it's largely close to right.

it always works if the 2 outside numbers add up to less than 10.

but there is another rule that it follows when the numbers equal 10 or more. so for instance, 319, 418, 627 are all divisible by 11 and don't pass the above test, but they'll pass this test - if you add up the outside numbers, and take away the larger number from the smaller number, it will equal the middle number.

so for instance

319.
3 + 9 = 12.
2 - 1 = 1.

418
4 + 8 = 12
2 - 1 = 1

627
6 + 7 = 13
3 - 1 = 2

759
7 + 9 = 16
6 - 1 = 5

it's a little harder to follow but it works. like you i'm almost certain all 3 digit numbers divisible by 11 follow one of those rules.
 

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