# Wild About Math!Making Math fun and accessible

26May/0812

## Warmup problems for Monday Math Madness #7

Blinkdagger has announced the winners for contest #6. A little later today I'll be posting contest #7.

In the meantime, here are a couple of warmup problems:

1. If a fish weighs one pound plus half its own weight, how much does the fish weigh? Do this problem quickly and without paper. I bet many of you won't get it right the first time. It's not a hard problem but it is tricky if you're not paying attention. Try this problem out on your friends.

2. What is interesting about each of the following pairs of numbers: (2,2) and (5/2, 5/3)?

Stay tuned for Monday Math Madness #7, later today. It's an interesting infinite series problem.

1. a spoiler for the second problem: another pair of numbers which could be used is (9/4,9/5).

2. Does that count for the first pair too? I mean, is the interesting thing about these pairs the same?

3. Johan,

Yes, the two numbers in the first pair have the same interesting relationship as the two numbers in the second pair. And, the hint from .mau. might help you as the pair (9/4,9/5) is also interesting in the same way.

4. Another pair: (-i, 1/2+1/2*i)

5. Sjoerd,

Very clever. I love it! Yes, that is another pair, although probably not helpful data for those who don’t see the pattern.

6. maybe with negative numbers it could be easier to spot the rule? (1, -1/2) is also ok, and even (0,0) is 🙂

7. Mau,

(1,-1/2) doesn’t follow the pattern. (0,0) does, though.

8. Is it 2

9. Sol,
I switched signs, indeed. I meant (-1, 1/2), of course!

10. The first thing I noticed was what you’re all obviously talking about.

The second thing I noticed was that the sum of the reciprocals was 1 (equivalently that both pairs have the same harmonic mean, of 2).

I then realized that the first thing and the second thing are equivalent…

So a way to get a whole lot of them:

[x, x/(x-1)]

11. ((a+b)/a, (a+b)/b) ?

12. What’s interesting about all the pairs of numbers is that a+b = a*b.