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Author Topic: Math Facts/Tricks  (Read 670 times)

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Offline Flame[1up]

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Math Facts/Tricks
« on: April 04, 2015, 12:36:15 AM »
I thought it might be an interesting way for me to study/relay information by posting any cool tricks or any weird math facts I know. (Maybe even in a daily manner)

Happy Numbers vs Sad Numbers
One of those things I have no clue why exists, but it does so here are the definitions
Happy Number- A number whose sum of its digits squared recursively will eventually go to 1
Sad(Unhappy) Number- A number whose sum of its digits squared recursively will never go to 1 (Not a happy number)

For example take the number 7:
72=49
42+92 = 16+81 = 97
92+72 = 81+49 = 130
12+32+02 = 1+9+0 = 10
12+02 = 1+0 = 1
So 7 is a happy number  :D

25 is a sad number, the work is:
22+52 = 4+25 = 29
22+92 = 4+81 = 85
82+52 = 64+25 = 89
82+92 = 64+81 = 145
12+42+52 = 1+16+25 = 42
42+22 = 16+4 = 20
22+02 = 4+0 = 4
42=16
12+62 = 1+36 = 37
32+72 = 9+49 = 58
52+82 = 25+64 = 89
At this point the process repeats (We already did 89), so 25 is an unhappy number.

Note: Any number generated during a process which ends with a number being happy is happy, and any number generated during a process that ends with a number being sad is sad.
« Last Edit: April 04, 2015, 12:38:25 AM by Flame[1up] »
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Offline Cope57[1up]

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Re: Math Facts/Tricks
« Reply #1 on: April 04, 2015, 01:16:00 AM »
I am sad to know you would spend so much effort to determine if some numbers are sad or happy.

Now all you have to do is select the right combination of numbers to win a Lottery.
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Offline Fusion[1upZ]

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Re: Math Facts/Tricks
« Reply #2 on: April 04, 2015, 05:56:35 AM »
Quote from: Cope57[1up] on April 04, 2015, 01:16:00 AM
I am sad to know you would spend so much effort to determine if some numbers are sad or happy.

Now all you have to do is select the right combination of numbers to win a Lottery.
My thoughts exactly :P
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Offline Flame[1up]

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Re: Math Facts/Tricks
« Reply #3 on: April 04, 2015, 04:56:30 PM »
Special Case of Squares

Sometimes when adding two 2-digit squares you may find that the outside digits add up to 10 and that the one's digit of the first number is one bigger than the ten's digit of the second.

762+532=?
(Here the outside digits are 7 and 3 which add up to 10 and 6 is one greater than 5)

If this is the case you square the digits of the first number and add those together
72+62=49+36=85

Then multiply by 101:
85*101=8585

8585 is 762+532

Mathematical Proof of trick if wanted
Spoiler (click to show/hide)
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