Difference between revisions of "2019 AMC 10A Problems/Problem 10"
Ironicninja (talk | contribs) (→Solution) |
m (→Solution 2 (Troll)) |
||
| Line 12: | Line 12: | ||
Edit: The general formula is that because it is the number of vert/horz lines crossed minus the number of corners crossed (b/c that would be double counting). In this particular problem, it was 16 + 9 - 1 (gcd of 16 and 9 is 1), which is 24, but then you add two because the first tile and the last tile are counted, which in the general formula are not counted. | Edit: The general formula is that because it is the number of vert/horz lines crossed minus the number of corners crossed (b/c that would be double counting). In this particular problem, it was 16 + 9 - 1 (gcd of 16 and 9 is 1), which is 24, but then you add two because the first tile and the last tile are counted, which in the general formula are not counted. | ||
| − | ==Solution 2 ( | + | ==Solution 2 (Draw it out)== |
Draw it out using grid paper and a ruler. Carefully counting the squares gives us 26. | Draw it out using grid paper and a ruler. Carefully counting the squares gives us 26. | ||
Revision as of 20:29, 11 February 2019
Problem
A rectangular floor that is 
feet wide and 
feet long is tiled with 
one-foot square tiles. A bug walks from one corner to the opposite corner in a straight line. Including the first and the last tile, how many tiles does the bug visit?
Solution
The number of tiles the bug visits is equal to 
plus the number of times it crosses a horizontal or vertical line. As it must cross 
horizontal lines and 
vertical lines, it must be that the bug visits a total of 
squares.
Note: The general formula for this is 
.
Edit: The general formula is that because it is the number of vert/horz lines crossed minus the number of corners crossed (b/c that would be double counting). In this particular problem, it was 16 + 9 - 1 (gcd of 16 and 9 is 1), which is 24, but then you add two because the first tile and the last tile are counted, which in the general formula are not counted.
Solution 2 (Draw it out)
Draw it out using grid paper and a ruler. Carefully counting the squares gives us 26.
See Also
| 2019 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
