CMI2024-A: 3

Question

You live in $\Delta$-City, which is a large equilateral triangle with each side of length $2$ km. The corners are named $A, B$ and $C$. The city is partitioned into triangular blocks with sides of $500$ m each, and there are roads at the boundaries of the blocks.

You live in corner $A$ and your office is at corner $B$.

You have decided to walk from home to the office everyday, and you are willing to change your route, as long as the total distance is at most $2.5$ kms . How many such routes are possible from $A$ to $B$?

• A. $5$
• B. $11$
• C. $21$
• D. $45$

   

Answer 1

There are 2 ways one you can brute force it and get answer as 11.

Other is like a dynamic programming approach where you maintain an 2d array of no of ways to reach a particular point with starting at A with certain distance similarly maintain one for B and add every pt which leads to sum less than 6(6 edges make more than 2.5km) and get answer as 11. Still prefer brute force as its easy here

Answer 2