Math Is Fun Forum

1. How would you weigh a jet plane without using scales?

2. Why are manhole covers round rather than square?

3. Why is it that, when you turn on the hot water in a hotel, the hot water comes out instantly?

4. How do they make M&Ms?

5. How many times a day do a clock’s hands overlap?

6. You have eight billiard balls. One of them is “defective”, meaning that it weighs more than the others. How do you tell, using a balance, which ball is defective in two weighings?

7. You have two jars and 100 marbles. Fifty of the marbles are red, and 50 are blue. One of the jars will be chosen at random; then one marble will be withdrawn from that jar at random. How do you maximise the chance that a red marble will be chosen? (You must place all 100 marbles in the jars.) What is the chance of selecting a red marble when using your scheme?

8. You have a three-quart bucket, a five-quart bucket, and an infinite supply of water. How can you measure out exactly four quarts?

9. You have a bucket of jelly beans in three colours — red, green, and blue. With your eyes closed, you have to reach in the bucket and take out two jelly beans of the same color. How many jelly beans do you have to take to be certain of getting two the same colour?

10. Four people must cross a rickety footbridge at night. Many planks are missing, and the bridge can hold only two people at a time (any more than two, and the bridge collapses). The travellers must use a flashlight to guide their steps; otherwise they’re sure to step through a missing space and fall to their death. There is only one flashlight. The four people each travel at different speeds. Adam can cross the bridge in one minute; Larry in two minutes; Edge takes five minutes; and the slowest person, Bono, needs ten minutes. The bridge is going to collapse in exactly 17 minutes. How can all four people cross the bridge?

11. Why are beer cans tapered at the top and bottom?

12. How long would it take to move Mount Fuji?

There... now who wants to get me a job with M$?
And does calling it M$ instantly disqualify me from said job? ;-)

There's like 5 jokes there, which one don't you get?

I used the tree diagram method as well (first creating a table of what points each point can link to, then a tree going through those possiblities) and I got 19 different answer. Haven't had a chance to double-check them against the diagram, but they all look like they should work...
[EDIT: Nevermind, now I'm at 14... somehow in building my relations chart I listed S-B as a valid connection, which obviously isn't true. Now I need to find where I'm missing stuff instead!]

To figure this out, you have to do a couple steps.
- First, since the ratio is 7:2, you add those together to determine how many total "units" the timber can be broken into.
- Then divide the length by the number of units, to find the length of each unit.
- Then, simply multiplying the length of each unit by the number of units length you want to calculate will tell you how long that piece is.

Aha! This is what I've been looking for, the basic place where we're apparently having trouble speaking the same language... and it seems to have been right at the basic definition of an infinitely recurring decimal, which is obviously why we think so differently on the equality (or lackthereof) of 0.999...

Lets take it back one step further then, and avoid 0.999... for now, since by my understanding of things, it's a special case (not in yours obviously, but by picking a different infinitely recurring decimal for now, we can avoid that incongruity).

So, instead we'll deal with 0.888... as I understand what you're saying, when I look at 0.888... I'm actually looking at 0.8? And the difference between 1 and 0.888... is 0.2? Is that right?

Okay, then yes I believe that for all cases, infinitely recurring numbers don't end, by definition.

What number does "infinite/recurring 0.9" represent? (written out to 3 decimals is fine). What number does "infinite/recurring 0.1" represent? (again, to 3 decimals is fine)

What about 0.909090909090909090....? How do you represent that as starting as one decimal place?

What comes after the ... in this example?

What do you mean "the calculation infinitely repeats itself"? Why can't I multiple the number 0.000...1? You told me that 0.000...1 / 2 = 0.000...5 up above, so if I can divide it, why can't I multiply it? Also, when writing it down, please write it as 0.000...1, not (0.1), since (0.1) doesn't exist as a number, and makes me assume that you mean 0.(1), which is 0.111..., which is entirely different from 0.(0)1 or 0.000...1 that we're discussing.

To be clear, the () generally go around the part that is being repeated:
0.1 = 0.1
0.(1) = 0.111...
0.(0)1 = 0.000...1 (which most people would argue is impossible, as above, but for now I'm giving you the benefit of the doubt)
(0.1) = 0.10.10.10.1... (which obviously doesn't make sense, since you can't have an infinite number of decimals in a number, only 1)

I'm trying to understand the nature of the number 0.000...1 that you've proposed. What is 0.000...1 * 5?

Hey guys, can we please get away from the insults and back to the mathmatical discussion?

We're already having this argument and don't need to start it all over again, I was just explaining what Sekky meant by his statement.

Now if you could respond to my other question to you a few posts up, that'd be great thanks.

You do realize that your "proof" is the same as saying:
2 = 1 because 2 will always equal 1
Right?

I was just reading your answer the way it was written, because it's not the 0.2 that's recurring, it's just the 2, so it should be written as 0.222... = 0.(2), not (0.2).

Anyway, I correctly assumed what you'd really meant in the next line of my post, and then explained why that was wrong too... which you apparantly ignored.