Trick Math Question
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18-07-2017, 01:25 AM
Trick Math Question
Without using a calculator, can you figure out the following calculation within 5 seconds ?

999,999,999,999,999,999,999
X
999,999,999,999,999,999,999
=
999,999,999,999,999,999,998,000,000,000,000,000,000,001

We have (21) - 9's squared.
A friend of mine wasn't the first to discover this, but he saw the pattern recently while playing around with his calculator.

So if you wanted to do a nerdy party trick, you could.

As it turns out, when you take just about any number of 9's above 9 and square it, you get the same pattern.

99^2=9801
999^2 =998001
9999^2=99980001

999,999,999^2= 999,999,998,000,000,001

Big Grin

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19-07-2017, 02:45 PM
RE: Trick Math Question
Cool.

There's another one along the lines of:

111×111=12321
1111×1111=1234321
11111×11111=123454321
111111×111111=12345654321

The answer is always a palindrome counting up from 1 to the number of 1's you're multiplying. So with 111 x 111, there's three 1's so the answer is 12321.
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19-07-2017, 03:57 PM
RE: Trick Math Question
1 x 142857 = 142857
2 x 142857 = 285714
3 x 142857 = 428571
4 x 142857 = 571428
5 x 142857 = 714285
6 x 142857 = 857142
7 x 142857 = 999999

The digits rotate around up to 6; after 7 you take the first digit and last digit and add them to get the same sequence...
8 142857 1142856
9 142857 1285713
10 142857 1428570
11 142857 1571427
12 142857 1714284
13 142857 1857141
14 142857 1999998

eventually you get to adding the first 2 digits to the last 2, etc

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19-07-2017, 04:21 PM
RE: Trick Math Question
[Image: screen-shot-2011-05-23-at-9-58-39-pm.png]

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19-07-2017, 05:19 PM
RE: Trick Math Question
I learned another one today with the square of numbers that end in 5.

25x25= (2x2)+2 with a 25 on the end.
625

125x125 should equal (12x12)+12 with 25 on the end.
15,625

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19-07-2017, 07:39 PM
RE: Trick Math Question
(18-07-2017 01:25 AM)Rahn127 Wrote:  Without using a calculator, can you figure out the following calculation within 5 seconds ?

999,999,999,999,999,999,999
X
999,999,999,999,999,999,999
=
999,999,999,999,999,999,998,000,000,000,000,000,000,001

We have (21) - 9's squared.
A friend of mine wasn't the first to discover this, but he saw the pattern recently while playing around with his calculator.

So if you wanted to do a nerdy party trick, you could.

As it turns out, when you take just about any number of 9's above 9 and square it, you get the same pattern.

99^2=9801
999^2 =998001
9999^2=99980001

999,999,999^2= 999,999,998,000,000,001

Big Grin

Too bad most calculators only display 10 digits....

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