The 2nd Heaviest Marble

Logic Level 5

You are given 32 identical looking marbles, each of slightly different weights. You are given a balance that can only compare two marbles at a time. When you compare weight of two marbles, that constitutes 1 move. N is the minimum number of moves you require to find the 2nd heaviest marble. Find N...


The answer is 35.

Satyen Nabar by Satyen Nabar , 48, India

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1 solution

Satyen Nabar
May 29, 2017

Set up a tournament for the 32 marbles starting with 16 pairs, then 8 pairs, 4 pairs, 2 pairs, and finally 1 pair. That will give us the heaviest marble. Now the 2nd heaviest marble could have lost to the heaviest marble in any of these 5 rounds. So the next contest is between these 5 marbles and in 4 moves, we get our 2nd heaviest marble... N= 35

4 Helpful 1 Interesting 0 Brilliant 0 Confused

How do we know that this is the minimum number of moves? You have established that 35 is possible, but need to demonstrate why it is a lower bound.

Calvin Lin Staff - 4 years ago

You could have a minimum of 31...???? let 1 as the 3rd heaviest marble,32 as the heaviest and 31 as the 2nd heaviest.. 1/2,1/3,1/4,1/5..........31/1,32/31

Dennis Escobal Sabanto - 3 years, 4 months ago

i did similar thing similar. but little different from this. this is similar to a tournament. the winner is the top most person. the top most person has to defeat the second best in the tournament.

Srikanth Tupurani - 2 years, 3 months ago

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