In the floor of a particular kitchen owned by an abstract artist, each row of tiles to the right of the first row contains two fewer tiles than the row directly to its left. If there are nine rows in all and a total of 450 tiles in the floor, how many tiles does the leftmost row contain?  Choose the correct choice from the following answers.
A) 52 B) 58 C) 60 D) 64 E) 68
This question can be solved in a variety of ways: with algebra, by TESTing THE ANSWERS and by using a great Number Property shortcut involving consecutive integers.   We're given a few facts to work with:   1) There are 9 rows of tiles.   2) When going from 'left to right', each row contains TWO FEWER tiles than the one next to it.   3) There are a total of 450 tiles   We're asked how many tiles the left-most most row holds (meaning the one with the MOST tiles).   To start, 450 is divisible by 9, so we can figure out the AVERAGE number of tiles per row. That is 450/9= 
<gadget id="calculator">450/9</gadget>
<output>50</output>
50. Since we're dealing with a set of 9 consecutive integers that differ by 2 each, we know that the '5th row' will have 50 tiles (the average). Then we just have to 'add 2s' until we get to the first row...   50 +2 +2 +2 +2= 
<gadget id="calculator">50 +2 +2 +2 +2</gadget>
<output>58</output>
58.   Final Answer:   58
<result>B</result>
In the floor of a particular kitchen owned by an abstract artist, each row of tiles to the right of the first row contains two fewer tiles than the row directly to its left. If there are nine rows in all and a total of 450 tiles in the floor, how many tiles does the leftmost row contain?