Math Question

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1

<p>1.
On a square gameboard that is divided into n rows of n squares each, k of these squares lie along the boundary of the gameboard. Which of the following is a possible value for k?</p>

<p>I got this one right but I'm I want to see if my reasoning is good/what method other people would use. I figured first that n rows by n squares each means the shape is a square. Then to find the border you would multiply n by 4 then subtract 4 because of the corners. So k would have to be divisible by 4 and 52 was the only number that was indeed divisible by 4.</p>

<p>Anyways on to the question where I need more help in.</p>

<p>2.
A positive integer is said to be "tri-factorable" if it is the product of three consecutive integers. How many positive integers less than 1,000 are tri-factorable?</p>

<p>Believe it or not I got it right by doing it the long way but there has to be a shortcut.</p>

<p>I tried to find a trend in the changes between the products of the 3 consecutive integers but halfway through I was already 217 so I just kept doing it the long way until i reached a 1,000. I really hope there's a shortcut for this lol, there should be considering that was a lot of work for a level 4 problem.</p>

<p>Many thanks</p>

2

<h1>2: Since it’s 3 consecutive number’s all multiplied together with the product under 1000, you could deduce that 9<em>10</em>11 is the biggest you can get. Since that’s the max, you can assume that every other combination (such as 8<em>9</em>10 and 7<em>8</em>9) will all fit.</h1>

<p>So the answer should be 9.</p>

3

<p>Thanks so much! I just kinda started on the wrong end.</p>

4

<p>For the first one, you can simply “plug in” the first few values of n, and determine k in each case. For example, if n=3, we have k = 8. If n=4, k=12, etc. You will notice that you get multiples of 4.</p>