Calculating the resistance

A 4ohm, 8ohm, and 24ohm resistors are connected together. How would I connect these three resistors to obtain a resistance of 10ohms? How would I connect these three resistors to obtain a resistance of 8ohms? Please explain calculations.

For 10 ohms, you could have the 8 ohm and 24 ohm in parallel and add the 4 ohm in series, so you get...

Req = 4 + (8 * 24)/32 = 4 + 6 = 10 ohm


For 8 ohms, you could connect the 8 and 4 in series and have that parallel to the 24, so you get...

Req = (12 * 24)/36 = 8 ohms

if you put the 3 of them in parallel you will get 1/R = 1/4 + 1/8 +1/24
bring to the same denominator

1/R = 6/24 + 3/ 24 + 1 / 24
R= 24/10 = 2.4 which is smaller than 10 and than 8

if you put the 24 and 8 ohms in parallel in series with the 4 ohm you get
R = (1/24+ 1/8) ^ (-1) + 4 = 24/4 +4 = 10 ohms <---- 10 ohms

If you put the 8 and 4 in series and 24 in parallel with them you get
1/R = 1/24 + 1/12 = 24/3 = 8 ohms <---- 8 ohms