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Title: Math Contest Question Post by: aly0303 on Oct 31, 2021 A Shonk sequence is a sequence of positive integers in which
each term after the first is greater than the previous term, and the product of all the terms is a perfect square For example: \(2, 6, 27\) is a Shonk sequence since \(6>2\) and \(27>6\) and \(2\cdot 6\cdot 27=324\) or \(18^2\) a. If 12, x, 24 is a Shonk sequence, what is the value of x? b. If 28, y, z, 65 is a Shonk sequence, what are the values of y and z? Title: Re: Math Contest Question Post by: habiba on Nov 1, 2021 Content hidden
Title: Re: Math Contest Question Post by: bio_man on Nov 1, 2021 This is some next level math!
Using the same approach at @habiba, we get: (https://biology-forums.com/gallery/43/6_01_11_21_1_02_50.png) (https://biology-forums.com/index.php?action=gallery;sa=view&id=43611) Notice that I strategically chose numbers between the boundary that were divisible by 13, 5, and 7. I needed to do this so that they could become perfect squares. Any further questions, let us know. Title: Re: Math Contest Question Post by: aly0303 on Nov 1, 2021 That's amazing! Thank you both!!!
Can you help me with part (c) Quote c. Determine the length of the longest Shonk sequence, each of whose terms is an integer between 1 and 12, inclusive. Your solution should include an example of this longest length, as well as justification as to why no longer sequence is possible. Title: Re: Math Contest Question Post by: bio_man on Nov 3, 2021 Start with 12!
Write its prime factorization. Square root each of them to see if they're perfect squares. You know it's a perfect square if its exponent is even. Go from there :) |