You have nine brass rings, but three are actually gold. Can you pick these out using a balance scale three times at the most?
No.of ways of picking 3 rings out of 9
= comb(9,3) = (9*8*7)/(1*2*3) = 12*7 =84
A scale will give one of three results, that is:
Left one is heavier, two scales are equal , or right one is heavier.
So there are in total 27 results.
Now, 84/27 = 28/9 > 27/9 =3
Therefore, the balance scale must be used more than 3 times.
Accordingly, it is NOT possible to pick these out using a balance scale three times at the most.
Puzzle Thoughts
