full transcript

## Unscramble the Blue Letters

Let’s draw the chembar on a coordinate grid, with the Southwest corner at the point (0,0). The light passes through grid points with coordinates that are either both even or both odd. This is true even after it bounces off one or more walls. Another way of thinking about it is this: since the light travels at a 45 degree angle, it always crosses the diagonal of a unit square. teivarnlg 1 meter horizontally changes the x coordinate from even to odd or vice vsera. Traveling 1 meter vtlilacrey changes the y ctoroinade from even to odd or vice versa. Traveling diagonally – as the light does here – does both at once, so the x and y coordinates of any points the light passes through must be both even, or both odd. This oaobetvrsin is more pofuewrl than it seems. In particular, it means that we have a way to identify the kinds of points the light won’t ever go through If one of the coordinates is even and the other is odd, the lgiht will miss them. That means it’ll miss the top two corners of the room, since those points have one even and one odd coordinate. The Southeast corner is the only oitpon for the diffuser.

## Open Cloze

Let’s draw the _______ on a coordinate grid, with the Southwest corner at the point (0,0). The light passes through grid points with coordinates that are either both even or both odd. This is true even after it bounces off one or more walls. Another way of thinking about it is this: since the light travels at a 45 degree angle, it always crosses the diagonal of a unit square. _________ 1 meter horizontally changes the x coordinate from even to odd or vice _____. Traveling 1 meter __________ changes the y __________ from even to odd or vice versa. Traveling diagonally – as the light does here – does both at once, so the x and y coordinates of any points the light passes through must be both even, or both odd. This ___________ is more ________ than it seems. In particular, it means that we have a way to identify the kinds of points the light won’t ever go through If one of the coordinates is even and the other is odd, the _____ will miss them. That means it’ll miss the top two corners of the room, since those points have one even and one odd coordinate. The Southeast corner is the only ______ for the diffuser.

1. light
2. powerful
3. observation
4. traveling
5. versa
6. chamber
7. coordinate
8. option
9. vertically

## Original Text

Let’s draw the chamber on a coordinate grid, with the Southwest corner at the point (0,0). The light passes through grid points with coordinates that are either both even or both odd. This is true even after it bounces off one or more walls. Another way of thinking about it is this: since the light travels at a 45 degree angle, it always crosses the diagonal of a unit square. Traveling 1 meter horizontally changes the x coordinate from even to odd or vice versa. Traveling 1 meter vertically changes the y coordinate from even to odd or vice versa. Traveling diagonally – as the light does here – does both at once, so the x and y coordinates of any points the light passes through must be both even, or both odd. This observation is more powerful than it seems. In particular, it means that we have a way to identify the kinds of points the light won’t ever go through If one of the coordinates is even and the other is odd, the light will miss them. That means it’ll miss the top two corners of the room, since those points have one even and one odd coordinate. The Southeast corner is the only option for the diffuser.

## Frequently Occurring Word Combinations

### ngrams of length 2

collocation frequency
great chamber 2
southwest corner 2
light passes 2
vice versa 2
versa traveling 2

### ngrams of length 3

collocation frequency
vice versa traveling 2

## Important Words

1. angle
2. bounces
3. chamber
4. coordinate
5. coordinates
6. corner
7. corners
8. crosses
9. degree
10. diagonal
11. diagonally
12. diffuser
13. draw
14. grid
15. horizontally
16. identify
17. kinds
18. light
19. means
20. meter
21. observation
22. odd
23. option
24. passes
25. point
26. points
27. powerful
28. room
29. southeast
30. southwest
31. square
32. thinking
33. top
34. traveling
35. travels
36. true
37. unit
38. versa
39. vertically
40. vice
41. walls