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# Help with mathsy/logic question? watch

1. I have a square field which is exactly one hectare (100 m × 100 m). On Monday I was surprised to find 4 mushrooms growing in a 1 m square formation, in the centre of my field. On Tuesday the group of mushrooms had expanded to 16, which were all 1 m apart.
When I looked at the group of mushrooms today (Wednesday), it had expanded to 36.
If the area covered by mushrooms continues to expand at this rate, how many days (including today) will it be until my field is covered in mushrooms?
2. (Original post by ambiconspicguous)
I have a square field which is exactly one hectare (100 m × 100 m). On Monday I was surprised to find 4 mushrooms growing in a 1 m square formation, in the centre of my field. On Tuesday the group of mushrooms had expanded to 16, which were all 1 m apart.
When I looked at the group of mushrooms today (Wednesday), it had expanded to 36.
If the area covered by mushrooms continues to expand at this rate, how many days (including today) will it be until my field is covered in mushrooms?
3. Think I got it...
Spoiler:
Show

Hint: Find the nth term rule for the sequence
4. M=(2D)^2
5. Monday = 4
Tuesday = 16
Wednesday = 36

All square numbers.
4 = 2^2
16 = 4^2
36 = 6^2

2, 4, 6 = 2n (n = number of days)
Mushrooms = (2n)^2
(2n)^2 = 100^2
(2n)^2 = 10000
2n = 100
n = 50

Is that right?
6. (Original post by Nikey)
Monday = 4
Tuesday = 16
Wednesday = 36

All square numbers.
4 = 2^2
16 = 4^2
36 = 6^2

2, 4, 6 = 2n (n = number of days)
Mushrooms = (2n)^2
(2n)^2 = 100^2
(2n)^2 = 10000
2n = 100
n = 50

Is that right?
Not sure if OP's asking for help in which case you shouldn't give the full solution. However, if he is just posing it as a question to us then I got the same as you
7. (Original post by zeldor711)
Think I got it...
Spoiler:
Show

Hint: Find the nth term rule for the sequence

Ah! Got it haha thanks
8. (Original post by Nikey)
Monday = 4
Tuesday = 16
Wednesday = 36

All square numbers.
4 = 2^2
16 = 4^2
36 = 6^2

2, 4, 6 = 2n (n = number of days)
Mushrooms = (2n)^2
(2n)^2 = 100^2
(2n)^2 = 10000
2n = 100
n = 50

Is that right?
The question asks for the number of days from today, Wednesday, not the number of days for the spread to occur from nothing.
9. (Original post by Good bloke)
The question asks for the number of days from today, Wednesday, not the number of days for the spread to occur from nothing.
So then you'd minus 3 from 50, right?
10. (Original post by Nikey)
So then you'd minus 3 from 50, right?
The question includes the words 'including today', doesn't it?
11. (Original post by Good bloke)
The question includes the words 'including today', doesn't it?
Lmao didn't see that.
12. (Original post by Nikey)
Lmao didn't see that.
Well, reading the question carefully is always a good start. If you read it carelessly you may as well not bother.
13. (Original post by Good bloke)
Well, reading the question carefully is always a good start. If you read it carelessly you may as well not bother.
Yeah I know, my bad. Thanks, will read it properly in future.
14. (Original post by RDKGames)
So, shall I be "that guy" and note that the area is clearly not increasing at a constant rate, so who knows what will happen in the future...
15. (Original post by DFranklin)
So, shall I be "that guy" and note that the area is clearly not increasing at a constant rate, so who knows what will happen in the future...
Quite! But to put it in non-mathematical and practical terms that any farmer would understand, the edge of the fungus patch creeps outward from its epicentre one metre every day (which is fairly realistic).
16. (Original post by Good bloke)
Quite! But to put it in non-mathematical and practical terms that any farmer would understand, the edge of the fungus patch creeps outward from its epicentre one metre every day (which is fairly realistic).
Well, apart from the slightly unnatural spreading out in a perfect square (and therefore the corners moving outward at sqrt(2) metres every day).

Note also that the question implies the "initial scenario" is a 1m square perfectly in the center of the garden, which is growing by 2m a day. The "correct solution" should therefore arguably be 48.5 days.

Or, y'know, the person trying to set the question could have phrased it better in the first place...

Edit: oh, and why are we assuming the axes of the mushroom square and the garden are perfectly aligned...? (Although there's a STEP question with the same issue, which was raised, and the examiners subsequently asked essentially the same question without fixing the ambiguity )

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