A Riddle a Day -- 78 Logical and Mathematical Puzzles

Weekend Solution

Finally, I'm updating! It's been a busy week with lots of swimming (at least I only swam half the time I was scheduled to this afternoon, so today hasn't been too bad.) Here is an interesting explanation of the solution that I found on the web. It's definately much better than any explanation I could come up with, haha. (Once again, explanation is borrowed, not mine.)

I found it easiest to work the"evil" sentence in reverse. To begin, we know that at some point in the past, the uncle was 3 times the age of the monkey. This doesn't give their ages, but it allows for a unit of measure to be established. Whatever age the monkey is at this time, let's call that 1 unit (1u). So, how old was the uncle when he was 3 times as old as the monkey? The uncle was 3u.

The previous part of the sentence states that the monkey will someday be 3 times this past age that we just established. So how old will the monkey be? He will be 9u.

Next, the uncle used to be half as old as this future version of our monkey. So, the uncle used to be 4.5u.

This first (and sort-of final) part of the sentence is the trickiest. The uncle is currently twice as old as the MONKEY was when the UNCLE was 4.5u. Well, we know that they both age at the same rate, so we can extrapolate. If the monkey was 1u when the uncle was 3u, then a year and a half later when the uncle was 4.5u, the monkey must have been 2.5u. Thus, we know that the uncle is currently twice the age of 2.5u, making him 5u.

Now, we can figure out the monkey's current age using the same technique we just used. (when the monkey was 1u, the uncle was 3u, so now that the uncle is 5u, the monkey must be 3u)

We also know that adding their ages will equal 4. So:

3u+5u=4

8u=4

u=4/8

u=.5

This makes our monkey 1.5 years old, and his uncle 2.5

Now, to finish off this puzzle! The monkey's weight is the same as the uncle's age, so the monkey weighs 2.5lbs. And since they're suspended at equal distances, we know that they must weigh the same. This will help us weigh the rope

The final sentence of the puzzle is actually pretty simple. The weight of the rope (R) plus the weight of the uncle (U) is one-half again (more simply put, 1 1/2 times) the difference between the weight of the monkey (M) and that of the uncle plus the monkey (U+M).

R+U=1.5((U+M)-M)

R+U=1.5U Then, subtract U from both sides, and you get

R=.5U

So the rope is half the weight of the uncle, making it 1.25lbs, or 20 ounces. Knowing that each foot of rope is 4 ounces, we can establish the length of the rope at 5 feet.

I hope this was easy enough to understand. If nothing else, I learned how hard it is to parse out complex algebraic word problems in a concise, easy to comprehend way.

Whew, that was a lot. This was a complicated puzzle, easily the most complicated Weekend Challenge yet. It took me over a week to solve and when I did I was only halfway right. Enjoy today's riddle!