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# Current Year 12 Thread Mark VI

Discussion for A-Level students and for those choosing their A-Level subjects.

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1. Re: Current Year 12 Thread Mark VI
(Original post by Llewellyn)
This is another good question.

There are 32 coins randomly arranged on a table. 16 are Heads, 16 are Tails. You are sitting down at the table with a blindfold and gloves on. You can move the coins and you can invert them (so a tail becomes a head and vice versa). You have no way of telling which coins are heads and which are tails. You must create two groups of coins under these conditions. There must be the same number of heads in each group. How will you do this?

Hint:
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Consider a simplified version. Say you have 2 coins on a table, 1 head, 1 tail. How would you make sure you get two groups with an equal amount of heads?

And for 4 coins, 2 heads, 2 tails?

And for 32 coins?
Are they put down as heads and tails for you? (i.e 16 each and not random? like 10 tails and 22 heads. I got a bit confused there)

If it is split up for you then split them up into 16 each and flip one set over. I think? I don't think flipping both of them over would make much sense
2. Re: Current Year 12 Thread Mark VI
(Original post by chickenonsteroids)
Are they put down as heads and tails for you? (i.e 16 each and not random? like 10 tails and 22 heads. I got a bit confused there)

If it is split up for you then split them up into 16 each and flip one set over. I think? I don't think flipping both of them over would make much sense
They are already split into 16 tails and 16 heads when you start.

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Also, you are correct again
3. Re: Current Year 12 Thread Mark VI
(Original post by Llewellyn)
They are already split into 16 tails and 16 heads when you start.

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Also, you are correct again
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4. Re: Current Year 12 Thread Mark VI
(Original post by Heptapus)
I guess..

They are the best form of revision too - I just can't be bothered right now.. >.<
I find it hard to motivate myself to do biology/chemistry as they're just too long - 1hr45 each.

I have finally finished all of my ISAs! Today was my 10th.
5. Re: Current Year 12 Thread Mark VI
(Original post by ElMoro)
Guys, I'm going to a taster day tomorrow and we're going to have lectures. Do you think it'd be weird if I recorded them with a dictaphone?
No, everyone at taster days takes notes and no one would notice.

I went to one at Cambridge, and people were taking photos of the slides of the powerpoint about the admissions process.
6. Re: Current Year 12 Thread Mark VI

1. Why is almost every cover circular? e.g. Manhole cover, bottle lid, etc.

2. What was the original reason for all prices being set to one less than a round figure? e.g. £9.99 instead of £10.00 (It is not about the price "seeming" to be less)

3. There are 5 apples in a basket. 5 people each take one apple. How is it possible that there is still 1 apple left in the basket?

4. A policeman sees a van driver go the wrong way down a one way street, then stop by double red lines on the next road. The policeman did nothing, why?

5. A mother gave natural birth to two sons. These sons shared the exact same birthday in the same year, but they weren't twins. How is this possible?

6. A man has 2 cubes with numbers on their faces. Each day, he rearranges them so that they read the current day of the month. He must use both cubes for all days, so the 4th would be "04", the 12th would be "12", etc. What are the numbers on the faces that allow him to do this?
Last edited by Llewellyn; 08-05-2012 at 21:23.
7. Re: Current Year 12 Thread Mark VI
here's my attempt:

1. Why is almost every cover circular? e.g. Manhole cover, bottle lid, etc.

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I think it's because a circle has the largest area for a given perimeter, and also you can screw circles onto things but you can't screw a square shape onto anything. Circles also fit nicely in the hand for things like bottle lids.

2. What was the original reason for all prices being set to one less than a round figure? e.g. £9.99 instead of £10.00

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This might too obvious and wrong but I'm gonna go with the psychological effect which makes it seem considerably more then 1p less than the next whole number

3. There are 5 apples in a basket. 5 people each take one of the apples. How is it possible that there is still 1 apple left in the basket?

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I couldn't help but read chickenonsteroid's solution

4. A policeman sees a van driver go the wrong way down a one way street, then stop by double red lines on the next road. The policeman did nothing, why?

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Was the van an ambulance?

5. A mother gave natural birth to two sons. These sons shared the exact same birthday in the same year, but they weren't twins. How is this possible?

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They are two of a set of triplets (heard this one before). But I have a feeling when you have triplets+ then you can call any two of them twins but I dunno

6. A man has 2 cubes with numbers on their faces. Each day, he rearranges them so that they read the current day of the month. He must use both cubes for all days, so the 4th would be "04", the 12th would be "12", etc. What are the numbers on the faces that allow him to do this?

Spoiler:
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Cube 1: 0, 1, 2, 3, 4, 6
Cube 2: 0, 1, 5, 7, 8, 9
2 and 5 can be flipped over to form the other one
Last edited by Refrigerator; 08-05-2012 at 21:31.
8. Re: Current Year 12 Thread Mark VI
Please try to keep stuff in spoilers if possible
(Original post by Refrigerator)
here's my attempt:

1. Why is almost every cover circular? e.g. Manhole cover, bottle lid, etc.

[spoiler]I think it's because a circle has the largest area for a given perimeter, and also you can screw circles onto things but you can't screw a square shape onto anything. Circles also fit nicely in the hand for things like bottle lids.

2. What was the original reason for all prices being set to one less than a round figure? e.g. £9.99 instead of £10.00

Spoiler:
Show
This might too obvious and wrong but I'm gonna go with the psychological effect which makes it seem considerably more then 1p less than the next whole number

3. There are 5 apples in a basket. 5 people each take one of the apples. How is it possible that there is still 1 apple left in the basket?

4. A policeman sees a van driver go the wrong way down a one way street, then stop by double red lines on the next road. The policeman did nothing, why?

Spoiler:
Show
Was the van an ambulance?

5. A mother gave natural birth to two sons. These sons shared the exact same birthday in the same year, but they weren't twins. How is this possible?

Spoiler:
Show
They are two of a set of triplets (heard this one before). But I have a feeling when you have triplets+ then you can call any two of them twins but I dunno

6. A man has 2 cubes with numbers on their faces. Each day, he rearranges them so that they read the current day of the month. He must use both cubes for all days, so the 4th would be "04", the 12th would be "12", etc. What are the numbers on the faces that allow him to do this?

Cube 1: 1, 2, 0, 7, 8, 9
Cube 2: 1, 2, 3, 4, 5, 6
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1 Not quite.
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The perimeter is the key. A square cover will fall down a square hall, but a circular cover will never fall down a circular hole, because its perimeter is equal. Any other shape has a varying "radius" (distance from the centre) and so can fall down.

2- Yes, I'm looking for a different reason sorry, you're not wrong though.

4 - Nice solution. I hadn't thought of that. I had another answer in mind but that also works.

5 - Correct.

6 - Very close
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How would you do the 8th?

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3 isn't about the wording, all 5 people are different.
Last edited by Llewellyn; 08-05-2012 at 21:22.
9. Re: Current Year 12 Thread Mark VI
(Original post by Llewellyn)

1. Why is almost every cover circular? e.g. Manhole cover, bottle lid, etc.

2. What was the original reason for all prices being set to one less than a round figure? e.g. £9.99 instead of £10.00

3. There are 5 apples in a basket. 5 people each take one of the apples. How is it possible that there is still 1 apple left in the basket?

4. A policeman sees a van driver go the wrong way down a one way street, then stop by double red lines on the next road. The policeman did nothing, why?

5. A mother gave natural birth to two sons. These sons shared the exact same birthday in the same year, but they weren't twins. How is this possible?

6. A man has 2 cubes with numbers on their faces. Each day, he rearranges them so that they read the current day of the month. He must use both cubes for all days, so the 4th would be "04", the 12th would be "12", etc. What are the numbers on the faces that allow him to do this?
1.
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Is it not something to do with greatest area to perimeter ratio? Basically it's an efficient shape. And it looks nice I'm not too sure on how to word this one and it cant fall down stuff... like manholes and bottle lids but a rectangle could

2.
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So that the people at the till would have to open it to get the 1p coin with a £10 they could just keep it

3.
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5.
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Is this biological? I don't want to say and make myself sound stupid

I've probably got all of these wrong
Last edited by chickenonsteroids; 08-05-2012 at 21:23.
10. Re: Current Year 12 Thread Mark VI
(Original post by chickenonsteroids)
1.
Spoiler:
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Is it not something to do with greatest area to perimeter ratio? Basically it's an efficient shape. And it looks nice I'm not too sure on how to word this one and it cant fall down stuff... like manholes and bottle lids but a rectangle could

2.
Spoiler:
Show
So that the people at the till would have to open it to get the 1p coin with a £10 they could just keep it

3.
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Show

5.
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Is this biological? I don't want to say and make myself sound stupid

I've probably got all of these wrong
2 and 3 are correct. 5 is not biological.

Edit: 1 is also correct, your last sentence gives the correct answer.
Last edited by Llewellyn; 08-05-2012 at 21:27.
11. Re: Current Year 12 Thread Mark VI
(Original post by Llewellyn)
2 and 3 are correct. 5 is not biological.

Edit: 1 is also correct, your last sentence gives the correct answer.
I've updated mine, I think I've got 6 now but the temptation was too much and I read chickenonsteroid's solutions to the 1p and the apple one, definitely wouldn't have got the 1p one myself haha
12. Re: Current Year 12 Thread Mark VI
(Original post by Llewellyn)
2 and 3 are correct. 5 is not biological.
5.
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not biological eh? I'm gonna say she gave birth to two sets of twins and I don't think they'd both be called twins
13. Re: Current Year 12 Thread Mark VI
(Original post by Refrigerator)
6.
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Cube 1: 0, 1, 2, 3, 4, 6
Cube 2: 0, 1, 5, 7, 8, 9
2 and 5 can be flipped over to form the other one
Correct, and interesting, I hadn't considered that either.

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My solution was very similar though, it involved flipping 6 upside down to get a 9.

(Original post by chickenonsteroids)
5.
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not biological eh? I'm gonna say she gave birth to two sets of twins and I don't think they'd both be called twins
Correct (basically).

My solution to 4:
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the van driver was walking
Last edited by Llewellyn; 08-05-2012 at 21:38.
14. Re: Current Year 12 Thread Mark VI
(Original post by Llewellyn)

My solution to 4:
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the van driver was walking
15. Re: Current Year 12 Thread Mark VI
EMPA advice anyone? ( The written bit)
16. Re: Current Year 12 Thread Mark VI
(Original post by --emma--)
I find it hard to motivate myself to do biology/chemistry as they're just too long - 1hr45 each.

I have finally finished all of my ISAs! Today was my 10th.
Once I get hold of a computer, all form of revision goes out of the window.

Nice! I have only done one!
17. Re: Current Year 12 Thread Mark VI
(Original post by Heptapus)
Once I get hold of a computer, all form of revision goes out of the window.
So so true!
18. Re: Current Year 12 Thread Mark VI
(Original post by 4mar_ar5en4l)
So so true!
You missed out on all the fun logic stuff
19. Re: Current Year 12 Thread Mark VI
(Original post by Heptapus)
Once I get hold of a computer, all form of revision goes out of the window.

Nice! I have only done one!

2 physics, 3 chemistry, 5 biology.

20. Re: Current Year 12 Thread Mark VI
(Original post by chickenonsteroids)
You missed out on all the fun logic stuff
I'm actually pretty gutted that I missed them, argh

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Last updated: August 13, 2012
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