Math Is Fun Forum

lewis thodoman

Guest

need help finding formula connecting values

i really can`t do this, i tried and tried but i can`t!

c=3, p=6, n=4
c=2, p=8, n=4
c=1, p=10, n=4
c=0, p=12, n=4

all these values can be connected by a single formula
the question is how? what is it?

there`s also this one i can`t do either!

c=0, p=18, n=3
c=1, p=16, n=3
c=2, p=14, n=3
c=3, p=12, n=3

all these values can be connected by a single formula
the question is how? what is it?

thx in advance guys

and if possible how could i go about solving these kinds of problems instead of drawing a table of values?

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: need help finding formula connecting values

I.
c=3, p=6, n=4
c=2, p=8, n=4
c=1, p=10, n=4
c=0, p=12, n=4
c and p change both by 1's and 2's, so
let's make a line.
c = p (1st try)
3 2 1 0 is not 6 8 10 12 so let's flip c around small to big.
-c = p (2nd try)
-3 -2 -1 0 is 6 8 10 12, but they both go up, so let's add 6 and double it.
2(-c + 6) = p (3rd try)
Yup that worked.
p = -2c + 12 for c = {0,1,2,3} and n = 4 always.

II.
c=0, p=18, n=3
c=1, p=16, n=3
c=2, p=14, n=3
c=3, p=12, n=3
c and p both change by 1's and 2's again.
2c = p   (1st try)
0 2 4 6 is not 18 16 14 12
Add nine (2nd try)
9 + 2c = p
9 11 13 15 is not 18 16 14 12
Flip over the 2c and add 9 more.
9 + 9 - 2c = p
18 16 14 12, yup that worked.
p = -2c + 18 and n = 3 for c = {0, 1, 2, 3}

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