Math Is Fun Forum

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

Small problem of logic.

Hi, there's just one thing which I'm not sure with this problem :

There are 24 pounds of nails in a sack. Can you measure out 9 pounds
of nails using only a balance with two pans?

I answered yes and here's the reason. Consider a number X of nails which weights 24 pounds. This number X has atleast a factor of 2^3 (It can be higher.) in its factors. Why ? Because we need to divide evenly the number of nails so we can have equal weight on each side of balance.

So :
x/2=x/2

x/4=x/4

x/8=x/8

x/2=12 pounds x/4=6 pounds x/8=3 pounds

So we have the following groups (after successive divisons.):

x/2+x/4+x/8+x/8=x

Clearly, x/4+x/8 nails would give 9 pounds

Now, the only thing bugging me is that my solution is founded on the assumption that all nails must have equal weights. The question isn't clear if the nails do have all the same weight or not...

What do you think ???

THank you!

Last edited by Al-Allo (2014-08-01 11:59:44)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Small problem of logic.

hi Al-Allo,

Mathematical puzzles often have implied assumptions.  For example, with a real balance the fulcrum is not an infinitely small point which will mean that two weights that are close to each other in value, will appear to be in balance.  I think your assumption is perfectly reasonable and I like your solution.  You can 'cover yourself' by stating "I am assuming that ......."

Isn't it the case that your solution assumes that the nails can be split evenly once, then again, then again.  If you had unequal nails, it wouldn't matter, providing you do have 6 pounds and 3 pounds exactly.  The difficulty arises if you get one side slightly heavier but when you move one nail across to the other side, that now becomes the heavier side.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob