## Brain Teaser Chapter essay

The numbers need to be considered, are hey prime or composite numbers? Is the slope a factor in finding the answer? The first answer provided was to find out the number of squares the diagonal line goes through, first divide the L (length) of the rectangle by the W (width). This will n to be a whole number so rounding up necessary, then multiply that number by the W, which h provides an answer.

For example if the first rectangle W=2 and when seven is divided by two the answer is 3. 5. Round that number up to 4 and then multiply by (2 width) to GE t 8.

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If the and then divide four by three and get 1. 33 and round up to two. Multiply two by three and get six. This theory could work, however, one must ask how would you write an equate ion to tell someone to round up. If the answer yielded Ana even numbers then rounding would not be necessary. On the other hand, rounding may be needed for odd integers. Another theory to solve this question could be to multiply m by n and divide b y two.

This doesn’t work because in the ex. rectangle the diagonal passes through 8 sq rest.There are instances when this theory might work, but it is not a valid theory because it I s not sure to work every time. Initially, my first thought on how to solve this problem was to go through with the above theory, (multiply m by n, then divide by two), but this obviously does not work because the diagonal line passes through 8 squares, not 7. By definition, the GIF (greatest common factor), is the greatest factor or number that divides into two numbers.

When you beg in to look at it as 3GIF problem, it works every time because the number of units the line passes through will always have a GIF. The final theory used to determine the number of unit squares (1 x 1) that a d goanna passes through the rule is m+inch (highest common factor). The number of s squares the diagonal passes through when m and n are relatively prime is m+nil .

If a recta Engle was ex. then the equation would be 8+44, so the diagonal would pass through 8 aqua rest because the highest common factor of 8 and 4 is 4. This theory gives an accurate answer o n all occasions.

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