Some Hard Logic Riddles
Here are a two hard logic-based riddles to test your brainpower
on. I particularly like the elegance of the first one.
The Problem of the Brainwave CD Weights
You manufacture brain wave entrainment CDs for companies that
sell self-improvement products. You are at the post office, with
ten boxes of them ready to close up and ship out, but you have
a problem. Nine of the boxes contain CDs that are designed to
put the listener into an "alpha" or relaxing state,
and one is full of CDs that are designed to put the user into
a deeper "delta" state, for deep sleep. They look identical,
and you forgot to label them.
There is one difference, however. You remember that the "alpha"
CDs weigh 13 grams, and because different CD "blanks were
used, the "delta" CDs weigh 15 grams. Unfortunately,
you can't feel the difference in weight by lifting them.
The post office does have a scale. It costs one dollar each
time you weigh something, though, and you want to keep your costs
down. How do you use the scale as few times as possible to determine
which are the "delta" CDs?
Weighing the Gold
You have 15 tiny gold bars and a balance scale. One of the
bars is lighter than the others, but you can't tell the difference
by feel. What is least number of times you could use the scale
to determine which one is the light one?
Hard Logic Riddles - Solutions
Riddle Number One
Believe it or not, you can determine which box has the "delta"
CDs in it by using the scale just one time. Here's how:
Label the boxes 1 through 10. Put one brainwave entrainment
CD from box number one on the scale. Then, on top of that, put
two CDs from box number two. Then put three from box number three
on those, four from box four, and so on.
There are now 55 brainwave entrainment CDs on the scale. Pay
the dollar and see what the total weight is. If they were all
13 grams, the total weight would be 715 grams (55 x 13). However,
you know that one or more of the CDs weighs 15 grams.
Subtract 715 grams from the total weight, and this gives you
the "extra weight" for the heavier CDs. Since you know
that they are each two grams heavier than the others, you can
divide this excess weight by two, and the result tells you how
many of the heavier Cd's are on the scale, and this number tells
you which box contains the "delta" CDs.
For example, if the weight is 727 grams, you would subtract
715 from this, leaving you with 12 grams of "excess weight."
Divide this by 2, and you know that there are 6 of the heavier
CDs on the scale. Since the number of CDs from each box coincides
with the number assigned to that box, you now know that box number
six has the "delta" brainwave CDs.
Riddle Number Two
Just put two gold bars on the scale, one on each side, and
if you get lucky one of them will be lighter. Accordingly, the
least number of times you could use the scale to find the light
one is one (watch that wording). You can guarantee that you'll
identify the light gold bar with three uses, however.
1. Put 7 gold bars on each side. If they are equal in weight,
the one left out is the light one. If unequal, go to step two.
2. Take the gold bars from the lighter side and put three
on each side. If they are equal in weight, the one left out is
the light one. If unequal, go to step three.
3. Take the gold bars from the lighter side and put one on
each side. One will be the light one, or if they are equal in
weight, the one left out is the light one.
For more hard riddles, logic puzzles, jokes, brainteasers,
and mental exercises visit the riddle
and puzzle index page.