Math Puzzles
 

I was part of a maths competition today. There were some freaky questions in it that I want to know the answer to and you guys are the only ones I can think that could solve them. I didn't understand half of the questions and ended up guessing half of the ones I knew how to do. We weren't allowed calculators, yet some questions still relied on trigonometry. One of my answers to a multiple choice question was tan60, but I didn't realise that was √3 until I checked on my calculator afterwards. I think I shaded in the √3 option, but I can't quite remember.

This was the last question, worth 10 marks out of 137.

"If sinX cosX + sinY cosY + sinX sin y + cosX cosY = 1 and cos(x - y) is the smallest possible, what is the value of 2x - y, expressed in degrees, that is closest to 360?"

I don't even understand that. I have never seen anything like it before and it just freaked me out.

That question seems much less tedious and interesting than this one, however:

"28 points are equally spaced around the circumference of a circle. What is the total number of triangles whose three vertices are from those 28 points and the size of one of the angles is twice the size of another?"

Go!

I was also part of this competition. Are you year 11 or 12, I'm year 12. I did not do any of the last 5, including this one, because they were so different and unusual to what I have seen before. I didn't have time to waste on this question when I would never have got a correct answer. (But I did have a 1 in 1000th chance.)
I don't remember the circle question, there was one similar if I remember correctly with 12 vertices and it asked for the number of chords for something...?
But yeah, It was pretty difficult...

I'm in year 11. It seems a bit strange to give the same test to year 11s and 12s, especially if it aims to stump year 12s. Most of the questions were probably obscure enough that the extra year doesn't make too much difference, but it's going to ensure I get a low ranking. The base -2 question was fantastic, although I wasted way too much time on it to still not get an answer.

That circle question was #27, too.

Is this the Westpac Maths Competition? Or perhaps have they renamed it at some point in the last decade.


My favourite question ever was "I have a pile of watermelons in a warehouse that weigh 20kg. I have determined that 99% of the weight of the watermelons is water. After a week sitting in the warehouse, some of the water has evaporated so that the watermelons are now 98% water. How much do they now weigh?"

I'll give posrep to anyone who gets it right. This one was quoted in the newspaper the day after the Westpac quiz as an example question. The day after that they needed to publish a lengthy explanation, as so many people had called in to complain that they thought the answer given was incorrect.

I'm assuming the people who got it wrong did so because they calculated the second weight using the original water mass. As in, they used the amount of water in every 1% of the first set of watermelons to make up the 98% of the second without taking into account the overall decrease in mass i.e. each 1% is now smaller.

Haven't done maths in a couple of years, but here we go.

20/100 = 0.2 (The weight of every 1%)
0.2 x 99 = 19.8 (The weight of the water)

100 - 99 = 1 (How much is actually melon)
0.2 x 1 = 0.2 (The weight of actual melon)

*Thinks* Hmm. If I can't reconstruct the second weight using the values I have now, I'm stuck. Not sure. Heh, only 200g of that 20kg pile of watermelons is actually melon. That's funny. Wait a minute. Melon doesn't evaporate. Even if the percentages change, the mass of melon flesh will stay the same. I ma gemius!

100 - 98 = 2 (The percentage of melon that the same mass of flesh now makes)
0.2/2 = 0.1 (How much each 1% is therefore now worth weightwise)

0.1 x 98 = 9.8 (The weight of the remaining water)
9.8 + 0.2 = 1 (The total weight of water and flesh)

Turn that percentage back into the original units...

1 x 100 = 1kg

Now to hear why I'm completely and utterly wrong.

EDIT: Darn, that 1kg doesn't look right. I always lose something along the way...

I failed maths in school, I've never been good at it, and personally stupid questions like that just piss me off because I get the feeling it's just some guy sat there laughing his ass off that he's made a question as pointless as it is ridiculous.

No... not MATHS! you know my weakness!

Yeah I completely suck at Maths. I retook GCSE Maths 3 times and failed every time.

Well, to begin with there is a total weight of 20kg - 200g of "dry melon" and 99 times that of water, or 19,800g. If after a week the water is down to 98%, the percentage that is dry melon must have risen to 2%. This means there is now 49 times as much water as melon, 9800g, and the total weight is 10kg.

You were on the right track until this point:

It was a bit redundant to multiply 0.1 by 98, then add 0.2. You could have just multiplied 0.1 by a hundred. But the point where you really went wrong was in saying that 9.8 + 0.2 = 1, instead of 10.

Ench wins the prize!

Fucking powers of 10. We need to convert to base-12, I'm telling you.

One of the questions in the maths quiz involved finding the number 2000 in base -2. The question was how many nonzero digits did that base -2 number contain.

I spent 10 minutes trying to force it before I just gave up.

What is base negative 2? Or do you mean base (hyphen) 2?

11111010000

It took me three minutes to add them up, but I am out of practice with arithmetic that isn't required for making change.

http://nobodyputsbabyinahorner.files...sion.gif?w=426

The appropriate response to this amount of maths

People really shouldn't turn off when exposed to maths. It's really not that difficult: most of it is nothing but following instructions.

And when you get down to it, Mathematics is the source code of the universe. That is too cool for school, but they try anyway.

Our teacher signed us up on a similar test yesterday. I'm not sure if it was the same one, but we weren't allowed calculators which made me realise I've relied on them too much. I'd forgotten most of my basic math skills from primary which made me realise I need to go home and do more practise. I only knew how to do half the questions, only attempted 2/3's of the questions and then gave up and randomly selected the last third.

I always found the non calculator papers easier.

I know my own head rather well, but I'm completely at sea with a scientific calculator.

I remember steadfastly refusing to shell out for a graphic calculator in sixth form for my statistics class, so I figured out how to crunch the numbers on my scientific.

Good thing it was just statistics. I'd like to see you try doing sin/cos/tan in your head.

SohCahToa.

That's not really the same as "sin 2 = 3.626860407847...".

Also, due to my age, "Sock a Toa" just causes me to imagine punching Tahu's mask off.

...

*makes frantic hand gestures*

I need to spread rep around before +repping you again.

Base negative 2 works like any other base. The catch is that every other power of -2 is negative and subtracts from your total value.

In that case the answer is 1100011010000.

I think you mean

http://blog.joerenken.com/wp-content...Of-Fuck-Wh.png

I am never going to use numbers of any kind. You hear me? NEVER.

Not in a thousand years.

That was a quick thousand years.

It literally ended as soon as it was mentioned.

Four men are in a boat on a lake. The boat capsizes and all four men fall into the water. However, not a single man got wet. Why?

Because there was more than a single man there?

Protip: Linguistic riddles aren't math problems.