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# Math Contest Question

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Posts: 105
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A month ago
 Math Contest Question A Shonk sequence is a sequence of positive integers in whicheach term after the first is greater than the previous term, andthe product of all the terms is a perfect squareFor 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? Read 50 times 4 Replies
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habibahabiba
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Staff Member
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Posts: 738
A month ago
 Ask another question, I may be able to help!

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wrote...
Educator
A month ago Edited: A month ago, bio_man
 This is some next level math!Using the same approach at @habiba, we get: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.
wrote...
A month ago
 That's amazing! Thank you both!!!Can you help me with part (c)Quotec. 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.
wrote...
Educator
A month ago
 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