Problem 2 · The spiral walk
Each 38-step cycle advances $(+1,+1)$; then handle the remainder.
Integer answer, at most 4 digitsIn a plane with the usual coordinate axes, we start at the point $(0,0)$ and move following a pattern: ten units right, ten units up, nine units left and nine units down. We keep repeating this pattern until we have moved exactly 2025 units. At which point do we end up? (Give the two coordinates in a row; for example, if the answer is the point $(28,49)$, answer $2849$.)
Copa Cangur · SCM
Medium
Closed answer
Reasoned solution
Key idea: a full cycle is $10+10+9+9 = 38$ units and leaves a net displacement of $(+1,+1)$.
$$2025 = 53 \cdot 38 + 11.$$
After $53$ cycles ($2014$ units) we are at $(53,53)$. With the remaining $11$ units: $10$ right to $(63,53)$ and $1$ up to $(63,54)$.
Answer: 6354