l>Problem solving ContestProblem addressing ContestbyLacey Walker, Rory Statham, D"laney Bruneau, Ryan Flegg and Blair Jasper
 Congratulations come the following students who entries were selected as winners in the recent middle level trouble solving contest. Our thanks to note Jensen the the mathematics department at the Melfort an extensive Collegiate because that judging the entries. Selections to be made ~ above the basis of accuracy, creativity, detail and also organization the the answers given.Problem 1In a polygon, a diagonal line is a line joining 2 non nearby vertices. A triangle has no diagonals. A quadrilateral has actually 2 diagonals. A pentagon has 5 diagonals. How plenty of diagonals would be in a 15 sided polygon?Winner - Lacey WalkerGrade 6 , Star City SchoolLacey"s prize - The first thing i did to fix this trouble was an alert a sample in the polygons that had an odd variety of sides. A triangle has 0 diagonals, a pentagon has 5 diagonals, a 7 face polygon has 14 diagonals, a 9 sided polygon has 27 diagonals. ( check out diagrams ). This is the sample that ns discovered: 3 sided: 3 x 0 = 0 5 sided: 5 x 1 = 5 7 sided: 7 x 2 = 14 9 sided: 9 x 3 = 27 11 sided: 11 x 4 = 44 13 sided: 13 x 5 = 65 15 sided: 15 x 6 = 90
Therefore, there are 90 diagonals in a 15 face polygon.Note indigenous The Centralizer: over there is a breakthrough of the expression behind Lacey"s sample in the Quandaries and Queries ar of Math central in a keep in mind titled Diaginals in a Polygon.Problem 2Paul areas 7 bags the marbles ~ above a table. The second bag has 2 much more marbles 보다 the first bag. The third bag has actually 4 more marbles 보다 the second bag. The 4th bag has 6 more marbles 보다 the 3rd bag and so on. The total variety of marbles in all seven bags is 231. How numerous marbles are there in each bag?Winner - Rory StathamGrade 7 , Star City SchoolRory"s prize - very first of all, to figure this inquiry I divided 7 into 231 and got 33. Since I got 33, ns knew that there couldn"t it is in any more than 33 marbles in the an initial bag. So I began with a smaller sized number prefer 14 in the first bag. I offered a chart and also the guess and also check an approach to find what numbers would job-related to obtain 231. Mine answers room 17, 19, 23, 29, 37, 47 and 59. (see chart)1st2nd3rd4th5th6th7th totalcheck
14162026344456 210no
151721273545 57217no
161822283646 58224no
171923293747 59231yes
Problem 5A sample is make of alternate red and black disks. The an initial row has actually only one disk, the second row has actually three disks, the third row has five disks and so on. Each heat begins and ends v a black disk. How numerous red disks space there in the an initial to fiftieth rows inclusive.Winner - D"laney BruneauGrade 6 , Star City SchoolD"laney"s prize - an initial of all, I attracted a snapshot to number out the question.

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