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its been a long time since i took high school and college math, but im very smart.

im trying to write an equation for the general description of a problem like this: you have a tile with x squares on it. you have a box with y number of crayons. you are going to color the tile. how many unique tiles can you make with your crayons if the exact position of each color doesnt matter.

like, if you have x=4, y=4, abcd for colors.

we would only count abcd once, instead of counting abcd and acbd as unique. ok?

so i figured out for one square there is a simple equation... 1,2,3,4,...

i also figured out how the equations are related.

my calc is too fuzzy and my factorials education is non-existant.

i know that the equation for the two boxes is the sum of the terms from the first equation. i also remember that handshake problem is (n)(n+1)(1/2) or (n^2+n)/2

i also know that the equation for the three box equation equals the sum of the sums, or the sum of the terms from the two box equation, which is the sum from n->1 of n.... for n=4, i know the third equations should give me something like... for 4 crayons;

since 1 box is 1,2,3,4; y=4. the second is 1,1+2,1+2+3,1+2+3+4, y=10

so the third is [(1)+(1+2)+(1+2+3)+(1+2+3+4)]=20 and i know its right.

the fourth should be then (1)+[(1)+(1+2)]+[(1)+(1+2)+(1+2+3)]+[1+1+2+1+2+3+1+2+3+4]=

should i start by factoring out a 1, then putting a plus, then factoring out a 2, then a plus, then factor 3...?

i want to put this in an equation in general terms of n=number of crayons with x=boxes on the tile, and y=total number of possiblities.

im really smart but i just cant see how to formulate the general equation, though i have no trouble calculating the specific answers for lower numbers.

HELP!