Teleportation

Computer Science Level 1

Alice is going to be late for school. As the map shows, a normal student would have to go through 6 paths to get there. Fortunately, Alice has a superpower to teleport to any nodes with the same color as her current node. She can use this power only once .

What is the least number of paths she needs to go through to get to school?

Clarification: The teleportation happens instantaneously and thus is not included in the count.

Harry is also late for school but he has better superpowers!

2 3 4 5

3 solutions

Jaya Krishna
May 22, 2017

The main thing to note is that you're allowed to teleport only once.

If you teleport from the first red to the other, then you can best make 4 moves to reach school
if you move from red to green and then teleport , you make 6 moves, not desirable at all
we can similarly count the number of moves required for each type but the least number of moves is when we move from red to green to red to blue and then teleport to school - taking only $\boxed{3}$ moves which is most desirable

You are correct. A common mistake is to get the shortest path and find the same color that is furthest apart. In this case: r-g-r-o-b-b-b, teleport on the red or blue color only reduce the length by 1, instead of 2 as your solution shows.

Christopher Boo - 4 years ago

Roger Erisman
May 17, 2017

Move to orange (2 moves)

Teleport to orange (0 moves)

Move to blue ( 1 move)

Teleport to blue(school) (0 moves)

2 + 1 = 3

This solution is flawed. Note that Alice can only teleport once!

Christopher Boo - 4 years ago

Jason Kelly
May 14, 2017

Impossible! You're welcome 😊

Can you write a solution that is helpful to those who cannot solve it? Else I'm inclined to delete this solution to encourage others to contribute a relevant answer.

Brilliant Mathematics Staff - 4 years ago

It's not impossible. Alice can travel downward to the green node then upward to the red node (not the one she started with, the one across from the green node). She is then able travel to a blue node. Her destination is also a blue node, which would allow her to teleport to school after only three moves.

Syd Antoine - 4 years ago

I couldn't solve it, but there were no proposed solutions at the time of my comment. My strategy therefore was to declare it impossible, which triggers a 'challenge-like' attitude from observing users that want to disprove my 'analysis,' like Sabrina has now demonstrated. Thanks Sabrina! 😊

Jason Kelly - 4 years ago

Oh and I've just realised from Sabrina's solution. I thought the teleportation itself counted as a move, which would have made it 4. If not then 3 works with that route.

Jason Kelly - 4 years ago

Teleportation

3 solutions

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