You have 4 weights weighing 2,3,5 and 7 pounds. The problem is none of them are marked. What is the fewest number of weighings you need using a balance scale figure out which weights are which?

I can get 3 weighings...
only two weight combos will give you a balanced...balance =)

2+3=5 and 2+5=7

once you have a balance, it's logical that the two weights are each lighter than the single heavy weight, so you know the single heavy weight is either the 5 or 7. (first weighing)

measure the lighter weights to see which is heavier of the two... the lighter weight will be the 2... the heavier of the two will either be 3 or 5. (second weighing)

put the 2 on one side of the scale and put the single heavy weight on the other (which will be either the 5 or 7) now put the second combination weight with the heavy weight (which will either be the 3 or 5)... so the 2 is on the left and the right will weigh either 12 (7+5) or 8 (3+5) now put the remaining weight with the 2 (which will either be a 7 or 3) if the remaining weight was a 7 then it'll be heavier because 7+2 = 9 and 9>8 but if the remaining weight is a 3 then the left will be lighter because 5<12 (third and final weighing)

so what do you guys think? I think it works just fine =D

Posted by Vina on 2004-07-25 22:42:50