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 and27>6 and 2*6*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?
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.
d. A sequence of four terms a,b,c,d is a super-duper-Shonkolistic sequence (SDSS) exactly when a,b,c,d and a,b,c and b,c,d are a Shonk sequence. Determine the number of pairs (m, n) such that m, 1176, n, 48400 is an SDSS.
This question was taken directly from the Grade 9 Fryer Contest for the University of Waterloo. Permission has been granted to discuss these questions online as the contests are officialy over.
I'd like to know the answers and the steps of the solution. Thanks.