3
$\begingroup$

What's the least amount of weighings you'd need to be able to successfully determine the weights of 4 balls weighing 1, 2, 3 and 4 kilograms, using a balance scale (counting the worst scenario)?

Any amount of balls can be placed on a single side of the scale.

$\endgroup$
1
  • 1
    $\begingroup$ Looking at the 2 answers here so far, can we please have a clarification: Are we able to put more than one ball on each side of the scale? $\endgroup$ – Chronocidal Apr 27 '20 at 15:11
2
$\begingroup$

A simple / basic answer, to provide an Upper Bound, is to use the scales

4 times

First, label our unknown balls "A", "B", "C", and "D". Next

Weigh them in pairs, and write down the winning pairs:
A&B v C&D
A&C v B&D
A&D v B&C

If, for demonstrative purposes, we assume that A=1, B=2, C=3 and D=4, then you would get this table:

1&2 = 3 v 3&4 = 7
1&3 = 4 v 2&4 = 6
1&4 = 5 v 2&3 = 5 : If we get the other 2 first, then we can skip this one!

We can then tally up each ball by "Heavy" versus "Light"

1: Light / Light / Draw
2: Heavy / Light / Draw
3: Heavy / Light / Draw
4: Heavy / Heavy / Draw

This means that our final step is

Compare the 2 balls with 1 "Heavy" and 1 "Light", to work out which is 2 and which is 3

$\endgroup$
3
  • $\begingroup$ With the update I have deleted my answer as it is no longer correct. This seems to be the optimal stratergy with the rules now being clarified :) $\endgroup$ – Beastly Gerbil Apr 27 '20 at 15:39
  • $\begingroup$ @BeastlyGerbil It's a pity that Puzzling isn't suitable for having a "sandbox" like Worldbuilding does to spot those queries slightly earlier ^_^' And, I certainly can't find a way to knock a number off at the moment $\endgroup$ – Chronocidal Apr 27 '20 at 15:54
  • 1
    $\begingroup$ There is no approach that guarantees success in fewer tests. Simple brute force on the three possible non-trivial first tests shows this. $\endgroup$ – user3294068 Apr 27 '20 at 16:58

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.