Lakitu’s Hidden Boost Setting
On a straight Mario Kart practice track, the checkpoints are numbered 0, 1, 2, 3, and so on. Mario starts at checkpoint 0. Every mini-turbo moves him forward exactly 4 checkpoints.
Every Mushroom moves the same hidden whole-number distance. That distance is more than 4 but less than 11 checkpoints. Mario may reuse either move in any order and may stop after any move.
Lakitu says, “Checkpoint 17 is the greatest-numbered checkpoint Mario cannot land on exactly.”
Lakitu’s practice track
Known move shown · Mushroom landing stays hidden
Test the hidden Mushroom setting
| Setting | Can 17 be reached? | Evidence |
|---|---|---|
| 5 | ||
| 6 | ||
| 7 | ||
| 8 | ||
| 9 | ||
| 10 |
Mushroom setting: ______
Your challenge
- How many checkpoints does one Mushroom move Mario? Prove that no other allowed setting can make Lakitu’s statement true.
- For your setting, prove that Mario cannot land on checkpoint 17 and that he can land on every checkpoint greater than 17.
Record settings 5–10 here. Use separate paper for your proof with number-line jumps or multiplication equations. Checking only a few checkpoints is not a proof.