coolio equation

so , mister cheng taught us how to use microsoft word to make
MATH EQUATIONS ! how cool :D



to solve this equation ::
first , i flipped the negative exponent (x^-2) to the top
then , the exponent is distributed 3/2 to all components
basically 3/2 means cubing a number then taking the square root of it
also goes for the x term .. so 9/2 becomes the square root of x to the power of 9
lastly , x can be changed into a mixed radical
TAADAA !



to solve this equation ::
first , flip the negative exponents ( y^-4 and x^-2 ) to the opposite side
then , distribute 5/2 to all the components
5/2 means taking the 5th power of a number then taking the square root of it
after multiplying the powers , the same goes for the x and y terms ..
20/2 becomes the square root of x to the power of 20
and 10/2 becomes the square root of y to the power of 10
finally , x and y are radicals and they can be simplified
.. they become x^10 and y^5

THE END !

favourite math question number.two

23) The numbers 123 456 789 and 999 999 999 are multiplied. How many of the digits in the final result are 9's ?
123456789
x999999999
_____________
1111111101
1111111101
1111111101
1111111101
1111111101
1111111101
1111111101
1111111101
1111111101
__________________
123456788876543211

[ its difficult to show the places exactly and they dont line up , but i hope this shows what i mean ]

first , i multiplied 123 456 789 x 9 = 1 111 111 101
then added them 9 times ; each time moving it forward one decimal space

the final answer was 123456788876543211
which concluded that there were no 9s

i chose this question because it looked really interesting
and it seemed challenging
( 123456789 x 999999999 )
i liked the question becuase it had a pattern
( 12345678887654321 )
and the question was fun to figure out

my favourite math problem :)

my favourite math problem was number seventeen ..

17) The digits 1 , 2 , 3 , 4 can be arranged to form 24 different 4-digit numbers. If these numbers are then listed from smallest to largest , what postition is 3142 ?

The numbers from smallest to largest are ::
1234 , 1243 , 1324 , 1342 , 1423 , 1432
2134 , 2143 , 2314 , 2341 , 2413 , 2431
3124 , 3142 , 3214 , 3241 , 3412 , 3421

3124 is the 14th number.

i solved this by writing out all the possible combinations of the four digits
as i listed them , i also put them in order from smallest to largest ..
therefore concluding that 3124 is in the 14th position

i liked this question because you have to make combinations of numbers
and thats fun :P
it wasnt hard to figure out
but i chose this question because of the different numbers
and it requires a bit of thinking and organization

tower of hanoi

describe the strategy and the formula for the tower of hanoi puzzle ::

basically ,
the objective of the puzzle was to move all the pieces from the left pole
to the right in the least possible amount of steps ..
as you can see , i have completed it in 36
while the minimum number of steps is actually 31 ..
anyhow , basically i just used trial and error and in the end ,
somehow , got all the pieces onto the right side ..
the most important thing is moving the top pieces
but not blocking or preventing the movemnet of the last piece ..

my strategy was moving the first piece to the middle pole
( in order to not block the other pieces from moving there )
then going back and forth and stacking the pieces in the middle
so that i could move the last piece to the third pole