Sliding robot
A robot moves along the number line. Where will it be after 2011 slides?
Age
11 to 14
Challenge level
Problem
A robot moves along the number line.
It starts at $0$, slides forward one unit (to $1$), slides backwards $2$ units (to $-1$), then forward $3$, back $4$, and so on.
It slides alternately forward and backwards, with each slide one unit longer than the previous one.
Where is the robot after $2011$ slides?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: 1006
| Slide number | Slide | Finish on |
| 1 | +1 | 1 |
| 2 | -2 | -1 |
| 3 | +3 | 2 |
| 4 | -4 | -2 |
| 5 | +5 | 3 |
| 6 | -6 | -3 |
| it is easier to see the pattern with even slide numbers | ||
| 2010 | -2010 | -2010$\div$2 = -1005 |
| 2011 | +2011 | 1006 |