pascal's pyramid question

[furyshade]

hey, i just learned of pascal's pyramid, yet cannot find any diagram of the 5th power of it. i built most of it on my own because i figured the pattern out from previous trangle, but the middle is getting me

| | | | | | 1| | | | | |

| | | | | 5| | 5| | | | |

| | | |10| |20| |10| | | |

| | |10| | | | | |10| | |

| | 5| |20| | | |20| | 5| |

| 1| | 5| |10| |10| | 5| | 1|

i have managed this, how do i solve the rest?

spacing got screwed up somehow when i posted it, but you can figure out what it is supposed to look like

[arahant]

ah, i see...hope no one replied yet!
looks like you have it wrong, though...google.

[furyshade]

this is pascal's pyramid, not pascal's triangle, each row is a coefficient fo a trinomial, this is one to the 5th power, it has very different properties though does have some similiarites to pascal's triangle

[arahant]

Glad you didn't 'quote' me /images/graemlins/smile.gif

[furyshade]

i looked on google and could only find to the 4th power

[furyshade]

figured it out, it is 30,
(x+15)*10^6+(x+21)*10^5+(x+15)*10^4=50,550,000

once i figured i needed this equation it was easy

[DJ Sensei]

if you want to look at it from a more practical manner, each entry in the pyramid is the sum of the 3 numbers "above" it in the previous level.

previous level is...

----1
---4 4
--6 x 6
-4 x x 4
1 4 6 4 1

by symmetry, so x has to be ten, but of course that could be figured out by:

---1
--3 3
-3 6 3
1 3 3 1

and so on until you reach the lonely 1 at the top.

(oh, and obviously assuming that all the numbers outside the pyramid are zero)

[tshort]

[ QUOTE ]
if you want to look at it from a more practical manner, each entry in the pyramid is the sum of the 3 numbers "above" it in the previous level.

previous level is...

----1
---4 4
--6 x 6
-4 x x 4
1 4 6 4 1

by symmetry, so x has to be twelve, but of course that could be figured out by:

---1
--3 3
-3 6 3
1 3 3 1

and so on until you reach the lonely 1 at the top.

(oh, and obviously assuming that all the numbers outside the pyramid are zero)

[/ QUOTE ]

The three numbers "above" the x's are 3, 6, 3.

[DJ Sensei]

so they are... so x is 12... so the missing number should be 36? thats weird...

i wish i had my old work on all this. the sides of each level's triangle are obviously correlated to rows of pascals triangle, but the middle is different stuff.