Why can’t I get that star?

This Christmas I got Super Mario Party for the Nintendo Switch, and if you’ve never played the game before, I suggest you try it at least once. It’s like a frustratingly hard board game where you can cheat to win…

And speaking of frustrating, one of the more difficult game modes I found was ‘Partner Party’.

In Partner Party, you team up with another player (or the CPU if nobody wants to play with you :|) to get the stars on the map, but unlike other game modes, you can move anywhere on the map.

It gets better, because in order to get the star, you have to land exactly on the square next to Toadette.

You have to land on Toadette’s square to get the star.

You find yourself in this situation where you roll the dice, but you can’t quite figure out how to get the star.

For example, let’s suppose that you’re exactly 1 move away from the star, and your team rolls an 8. Can you reach the star?

Dry Bones is only 1 move away from the star.

Don’t drive yourself crazy trying to find a path that moves you 8 spaces, landing on the star. It’s not possible and I’ll tell you why.

First, realize that any path that takes you back where you started took an *even* number of steps. See the screenshot below and count the number of red arrows I drew.

Any path that takes you back to the origin, moved an even number of steps.

In general, any path that takes you back where you started will have taken an even number of steps. Why? Because for every time you moved left, you moved right. And for every time you moved up, you also moved down. Therefore, the path that brings you back where you started took an *even* number of steps.

Bowser is confused.

Ok, so file this fact somewhere in your brain, and let’s go back to the example. You need your final move to land on the square with the star, which is only 1 move away! Your team rolled an 8. Now, let’s suppose that you found a path taking 8 steps that lands you on the star… but wait. There’s a problem!

If you move 1 more space to the right you will be back where you started. And what’s 1 + 8? That number is 9, which is NOT an *even* number. What you did was impossible, since any path that brings you back where you started takes an *even* number of steps. Hence, the supposition was wrong and you could not travel to the star in 8 steps.

Bowser Jr. is angry.

Don’t get angry. It’s a fact of life. In general, if the star is an *odd* number of steps away, you can never reach it by making an *even* number of moves.

You can make a similar argument to show that you can’t reach the star in an *even* number of moves if you rolled an *odd* number.

I hope you enjoyed reading my little argument. If you found some flaw in my reasoning, please don’t hesitate to correct me. In the off chance that you enjoyed reading this, please share with your friends. :)