This was a difficult puzzle. I got two correct answers – From Suman Saraf and Anahat (Prakhar’s son). Well done, or rather – excellent!
Here is the solution for 5 weights – copying solution from Suman.
let’s say the weights are w1, w2, w3, w4, w5
w1 and w2, let’s say w1 wins
w3 and w4, let’s say w3 wins
weight w1, w3, let’s say w1 wins
after 3 weighings we know w1 > w3 > w4 and w1> w2
now we compare w5 with w3 and depending on the result, compare with w1 or w4. After these, we would have w1, w3, w4 and w5 in some rank order, possible options are:
w5 > w1 > w3 > w4
w1 > w5 > w3 > w4
w1 > w3 > w5 > w4
w1 > w3 > w4 > w5
All that now remains is to put w2 in the right place.
In either of the above options, 2 comparisons (like we did in the step above) will lead to the right placement, since we already know w2 < w1
Hope you all enjoyed the puzzle!