I found a way to square 2 digits with an add...
11 x 11 = 121
0101 < square each digit and make them all 2 digits
1 + 1 = 2 * 10 = 20
0101 + 20 = 121 < correct answer
23 x 23 = 529
0409 < square each digit and make them all 2 digits
3 + 3 = 6 x 20 = 120
0409 + 120 = 529 < correct answer
Instead of cross mul , you add the last digits and mul by the first digit and add..
If you squaring 43 , then you add 3 + 3 and mul by 40 and add it to the squared digits..
If you squaring 92 , then you add 2 + 2 and mul by 90 and add it to the squared digits..
Now , on to figure 3 digit squares..
Number Trick
Re: Number Trick
With 123 ( 3 digits )
123 x 123 = 15129
010409 < square each digit and make them all 2 digits..
15129
10409

4720
23 + 23 x 100 = 4600
3 + 3 x 20 = 120
4600 + 120 = 4720
10409 + 4720 = 15129 < correct answer...
123 x 123 = 15129
010409 < square each digit and make them all 2 digits..
15129
10409

4720
23 + 23 x 100 = 4600
3 + 3 x 20 = 120
4600 + 120 = 4720
10409 + 4720 = 15129 < correct answer...
Re: Number Trick
With 246 ( 3 digits )
246 x 246 = 60516
041636 < square each digit and make them all 2 digits..
60516
41636

18880
46 + 46 x 200 = 18400
6 + 6 x 40 = 480
18400 + 480 = 18880
41636 + 18880 = 60516 < correct answer
246 x 246 = 60516
041636 < square each digit and make them all 2 digits..
60516
41636

18880
46 + 46 x 200 = 18400
6 + 6 x 40 = 480
18400 + 480 = 18880
41636 + 18880 = 60516 < correct answer
Re: Number Trick
it was a waste of time....You have to cascade add again...
1234 ( 4 digits )
1234 x 1234 = 1522756
01040916 < square each number and make them all 2 digits..
234 + 234 x 1000 = 468000
34 + 34 x 200 = 13600
4 + 4 x 30 = 240
With 2 digits we have 1 add
With 3 digits we have 2 adds..
With 4 digits we have 3 adds..
468000 + 13600 + 240 = 481840
1040916
+481840

1522756 < correct answer
So a million digits would require 999,999 adds... I got to invent a faster formula....
1234 ( 4 digits )
1234 x 1234 = 1522756
01040916 < square each number and make them all 2 digits..
234 + 234 x 1000 = 468000
34 + 34 x 200 = 13600
4 + 4 x 30 = 240
With 2 digits we have 1 add
With 3 digits we have 2 adds..
With 4 digits we have 3 adds..
468000 + 13600 + 240 = 481840
1040916
+481840

1522756 < correct answer
So a million digits would require 999,999 adds... I got to invent a faster formula....
Re: Number Trick
Another trick, I just invented..
I only tried on these 2 numbers ( i''l have to play around with different numbers )
12 x 14 = 168
0104 < square first number 12 , and make each digit into 2 digits
0116 < square second number 14, and make each digit into 2 digits
add them
104
116

220
12 + 14 = 26 x 2 = 52
220  52 = 168 < correct answer.
it only requires a x 2 multiply , other than the squaring part..( you can do the squaring part , on a million digits , in a couple seconds.. )
I'll have to try in on different 2 digits , and different lengths of digits.....
I only tried on these 2 numbers ( i''l have to play around with different numbers )
12 x 14 = 168
0104 < square first number 12 , and make each digit into 2 digits
0116 < square second number 14, and make each digit into 2 digits
add them
104
116

220
12 + 14 = 26 x 2 = 52
220  52 = 168 < correct answer.
it only requires a x 2 multiply , other than the squaring part..( you can do the squaring part , on a million digits , in a couple seconds.. )
I'll have to try in on different 2 digits , and different lengths of digits.....

 Posts: 649
 Joined: Jun 09, 2005 0:08
Re: Number Trick
@albert
Here's one I use on the 6502 since it doesn't have any multiply instruction, it uses pre calculated tables of squares so is quick to lookup with just some addition and subtraction
a*b=((a+b)²(ab)²)/4
Here's one I use on the 6502 since it doesn't have any multiply instruction, it uses pre calculated tables of squares so is quick to lookup with just some addition and subtraction
a*b=((a+b)²(ab)²)/4
Re: Number Trick
@StoneMonkey
I've filled a 500 page notebook in the last couple days , working on number manipulations...
The above 12 x 14 = 168 formula , only works on those 2 numbers.. I tried all different numbers and it doesn't work on other numbers..
I don't know how i do it ????
I come up with a formula using just the right numbers to make it work.. and other numbers don't work... I keep doing it..
Then i get the right answer , and go off all hog wild , celebrating.. And then it doesn't work on any other numbers...
I've filled a 500 page notebook in the last couple days , working on number manipulations...
The above 12 x 14 = 168 formula , only works on those 2 numbers.. I tried all different numbers and it doesn't work on other numbers..
I don't know how i do it ????
I come up with a formula using just the right numbers to make it work.. and other numbers don't work... I keep doing it..
Then i get the right answer , and go off all hog wild , celebrating.. And then it doesn't work on any other numbers...

 Posts: 649
 Joined: Jun 09, 2005 0:08
Re: Number Trick
@albert
Why not try making it a rule not to celebrate until you've tested further, see if you can break what you're doing using other values, write a program to test your functions and get it to loop through every possible combination to test your function and count how many times it passes/fails.
I might do something like this:
Why not try making it a rule not to celebrate until you've tested further, see if you can break what you're doing using other values, write a program to test your functions and get it to loop through every possible combination to test your function and count how many times it passes/fails.
I might do something like this:
Code: Select all
'multiply using lookup table of squares
'create global table of squares
dim shared as ushort table(0 to 511)
for i as long=0 to 511
table(i)=(i*i)shr 2
next
'multiply 8 bits by 8 bits=16 bits (unsigned) using table
function mul(byval a as ubyte,byval b as ubyte)as ushort
return table(a+b)table(abs(ab))
end function
'test
sub main
randomize timer
for i as long=0 to 20
dim as ubyte a=rnd*255,b=rnd*255
print a;"*";b;"=";mul(a,b);" ERROR=";mul(a,b)a*b
next
end sub
main
sleep
end
Re: Number Trick
@StoneMonkey
The formulas I'm working on , i can't write a program , till I've got several that match a rule..
So i have to do the manipulations on paper , until i get several sets of numbers working , with a particular rule..
Once i figure out the rule , then i can write a program...
The formulas I'm working on , i can't write a program , till I've got several that match a rule..
So i have to do the manipulations on paper , until i get several sets of numbers working , with a particular rule..
Once i figure out the rule , then i can write a program...
Re: Number Trick
I found an interesting formula..
44 x 44 = 1936

66 x 66 = 4356
22 x 22 = 484

4356  484 = 3872 x .5 = 1936
It doesn't work with other squares..
44 x 44 = 1936

66 x 66 = 4356
22 x 22 = 484

4356  484 = 3872 x .5 = 1936
It doesn't work with other squares..
Re: Number Trick
albert wrote:I found an interesting formula..
44 x 44 = 1936

66 x 66 = 4356
22 x 22 = 484

4356  484 = 3872 x .5 = 1936
It doesn't work with other squares..
Pay attention to your erroneous equality.
Rather:
4356  484 = 3872 = 2 * 1936
Let a = 66, b = 22, c = 44
a^2  b^2 = (a  b) * (a + b)
In your example:
a  b = c
a + b = 2 * c
Therefore:
a^2  b^2 = c * (2 * c) = 2 * c^2
Re: Number Trick
@fxm
44 x 44 = 1936

add 22 = 66 x 66 = 4356
sub 22 = 22 x 22 = 484

4356
 484

3872
x .5 or ( / 2 )

1936 < correct answer
I was trying to find a way to get the square of a even mul of 10..
And then divide by the difference..
But with big numbers the fraction to mul by equals would equal the number of original digits...
So if you want to find the square of 22 , you square 30 ( 30  22 = 8 ) and the mul by the fraction difference of 30 and 22...
44 x 44 = 1936

add 22 = 66 x 66 = 4356
sub 22 = 22 x 22 = 484

4356
 484

3872
x .5 or ( / 2 )

1936 < correct answer
I was trying to find a way to get the square of a even mul of 10..
And then divide by the difference..
But with big numbers the fraction to mul by equals would equal the number of original digits...
So if you want to find the square of 22 , you square 30 ( 30  22 = 8 ) and the mul by the fraction difference of 30 and 22...
Re: Number Trick
I now think that I should not have answered you because it is useless. So I stop right away.
Re: Number Trick
I got the formula finished...
123 x 123 = 15129
010409 < square each digit and make them all 2 digits..
15129
10409

4720 < difference
100 x 20 = 2000
100 x 3 = 300
20 x 3 = 60
2360 x 2 = 4720 < our difference. Since were multplying 2 sets , we need to double the output
10409
+ 4720

15129 < correct answer
123 x 123 = 15129
010409 < square each digit and make them all 2 digits..
15129
10409

4720 < difference
100 x 20 = 2000
100 x 3 = 300
20 x 3 = 60
2360 x 2 = 4720 < our difference. Since were multplying 2 sets , we need to double the output
10409
+ 4720

15129 < correct answer
Re: Number Trick
Listen, Albert: if you want a formula to square numbers, use this:
It works. Now, please, stop posting nonworking pieces of code.
Code: Select all
Exp(Log(X)*2)
It works. Now, please, stop posting nonworking pieces of code.
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