Addition Pyramid? Please Help!!

[helpplz]

I need to add the numbers one through nine together in a pyramid.
For example,
3 5 7 9 11 13 15 17
1 2 3 4 5 6 7 8 9
eg, 1+2=3, 2+3=5, 3+4=7......
Each number adds up the number next to it and it the levels increment untill it reaches the top.
The top of the pyramid, one number, is supposed to equal 1332. You can rearange the numbers 1-9 in any order using each once, but you cant change anything else. Please help! I don't understand it and I can't ask any adult figure for help.

I used an excel spreadsheet but all I can do is guess!
My parents aren't going to help me with my homework because they want to watch tv.

 

[tkhunny]

Not everyone will go visit a foreign link. You'll have to learn to communicate with words.

 

[soroban]

Hello, helpplz!

I don't blame your parents.
I'd rather watch "Gilligan's Island" reruns than work on this problem . . .

I need to add the numbers one through nine together in a pyramid.

For example,

. . \(\displaystyle \begin{array}{cccccccccccccccccc}&3 && 5 && 7 && 9 && 11 && 13 && 15 && 17 \\ 1 && 2 && 3 && 4 && 5 && 6 && 7 && 8 && 9 \end{array}\)

The top of the pyramid, one number, is supposed to equal 1332.
You can rearange the numbers 1-9 in any order using each once.

The addition is easier to see if we write the pyramid down the page:


. . \(\displaystyle \begin{array}{cccccccccccccccccc} 1&&2&&3&&4&&5&&6&&7&&8&&9 \\ & 3 && 5 && 7 && 9 && 11 && 13 && 15 && 17 \\ && 8 && 12 && 16 && 20 && 24 && 28 && 32 \\ &&& 20 && 28 && 36 && 44 && 52 && 60 \\ &&&& 48 && 64 && 80 && 96 && 112 \\ &&&&& 112 && 144 && 176 && 208 \\ &&&&&& 256 && 320 && 384 \\ &&&&&&& 576 && 704 \\ &&&&&&&& 1280 \end{array}\)

We see that the total is only 1280 . . . 52 short.

How can we "adjust" the intial row to get the required total?

I tried a number of approaches, but nothing seemed to simplify the problem.

 

[soroban]

I tried to generalize the problem . . .


\(\displaystyle \text{I used: }\:a,b,c,d,e,f,g,h,i\:\text{ for the first row.}\)


\(\displaystyle \text{The pyramid became:}\)

. . \(\displaystyle \begin{array}{cccccccccccccccccccc}a && b && c && d && e && f && g && h && i \\ & a+b && b+c && c+d && d+e && e+f && f+g && g+h && h+1 \\ && a+2b+c && b+2c+d && c+2d+e && d+2e+f && e+2f+g && f+2g+h && g+2h+i \\ &&&&&&&& \vdots \end{array}\)


\(\displaystyle \text{And the final number is: }\\). . . . . . . . . . . . . . . . . . . . \(\displaystyle a + 8b + 28c + 5d + 70e + 56f + 28g + 8h + i\)


\(\displaystyle \text{Using: }\:a=1,\;b=2,\;c=3,\:\hdots\;i = 9,\;\text{ the total is 1280.}\)

\(\displaystyle \text{Perhaps swapping two (or more) values will give us 52 more . . . ?}\)

 

[iambryanatkinson]

this question is actually very difficult to solve analytically

the better (and quicker) way to solve this question is to use programming
run permutation of 1 to 9 on a to i using soroban's solution and check which order gives 1332