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UKMT Maclaurin Olympiad 2022: Maths
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Wormscarf67
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#1
How did everyone find it? I didn't get q5 or 6, and was wondering if people had any insights?
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epii+1=0
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#2
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#2
(Original post by Wormscarf67)
How did everyone find it? I didn't get q5 or 6, and was wondering if people had any insights?
How did everyone find it? I didn't get q5 or 6, and was wondering if people had any insights?
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rasem005
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#3
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#3
(Original post by Wormscarf67)
How did everyone find it? I didn't get q5 or 6, and was wondering if people had any insights?
How did everyone find it? I didn't get q5 or 6, and was wondering if people had any insights?
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mqb2766
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#4
mqb2766
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#5
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#5
(Original post by Cridplbn)
Is the exam over now because I would like to see which ones I got right.
Is the exam over now because I would like to see which ones I got right.
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_wxyz_
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#6
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#6
I don't want to discuss it in detail yet until the paper and sols are out, but my solution for Q5 was not exactly inaccessible but it was pretty obscure (involving an interesting property of squares) - I assume there are more obvious ways of solving part (b), but I couldn't think of any alternative solutions. Q6 was easier imo but still a little tricky
edit: pretty sure its over so for q5 you can use the fact that b^2 and the two discriminants form an arithmetic sequence and for q6 a construction extending a line does the job
edit: pretty sure its over so for q5 you can use the fact that b^2 and the two discriminants form an arithmetic sequence and for q6 a construction extending a line does the job
Last edited by _wxyz_; 3 months ago
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Jam.123
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#7
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#7
What about for Q1? Me and the other person who did it from my school are both pretty sure it was impossible because the m% of water and losing (m-5)% of this to reach 50% water just doesn't work in our opinion
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_wxyz_
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#8
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#8
(Original post by Jam.123)
What about for Q1? Me and the other person who did it from my school are both pretty sure it was impossible because the m% of water and losing (m-5)% of this to reach 50% water just doesn't work in our opinion
What about for Q1? Me and the other person who did it from my school are both pretty sure it was impossible because the m% of water and losing (m-5)% of this to reach 50% water just doesn't work in our opinion
4 parts water to 1 part fruit becomes 1:1
(this comes from the quadratic m^2 - 205m + 10000 btw)
Last edited by _wxyz_; 3 months ago
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Jam.123
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#9
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#9
So m=80%:
80% - 80%(75%) = 20%
I feel like I'm just being stupid though
80% - 80%(75%) = 20%
I feel like I'm just being stupid though
Last edited by Jam.123; 3 months ago
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_wxyz_
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#10
Jam.123
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#11
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#11
(Original post by _wxyz_)
20% was the original weight of the non-water mass, so the new ratio is 1:1
20% was the original weight of the non-water mass, so the new ratio is 1:1
Thanks though
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cardtricks
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#12
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#12
how did you get that quadratic?Personally, I got m^2 - 105m 5000 which yielded no results so i was unable to solve the problem
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cardtricks
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#13
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#13
(Original post by cardtricks)
how did you get that quadratic?Personally, I got m^2 - 105m 5000 which yielded no results so i was unable to solve the problem
how did you get that quadratic?Personally, I got m^2 - 105m 5000 which yielded no results so i was unable to solve the problem
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Jam.123
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#14
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#14
20m^2-41m+20=0 is the final quadratic you'd need
(Original post by cardtricks)
sry m^2 - 105m + 5000
sry m^2 - 105m + 5000
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_wxyz_
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#15
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#15
(Original post by Cridplbn)
what was the explanation behind 6, I only had a couple of minutes to comprehend it and the only instinct I had was to use the abc conjecture. Any explanations
what was the explanation behind 6, I only had a couple of minutes to comprehend it and the only instinct I had was to use the abc conjecture. Any explanations
Last edited by _wxyz_; 3 months ago
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Jam.123
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#16
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#16
(Original post by Jam.123)
20m^2-41m+20=0 is the final quadratic you'd need
20m^2-41m+20=0 is the final quadratic you'd need
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Cridplbn
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#17
_wxyz_
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#18
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#18
(Original post by Cridplbn)
For question 2 we’re the answers 0 and 1
For question 2 we’re the answers 0 and 1
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_wxyz_
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#19
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#19
(Original post by Cridplbn)
Took a quick snap
Took a quick snap
Last edited by _wxyz_; 3 months ago
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Jam.123
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#20
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#20
expand (x+1)(x^2-x+1)
and then use this to find all the places where a power of two is one more than a cube
and then use this to find all the places where a power of two is one more than a cube
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