---
tags: 
parents: "[[MOCS/Puzzles|Puzzles]]"
date/time: 2024-10-15T22:32:00
---
vsco




### Knight Moves 6

[![](https://www.janestreet.com/puzzles/october-2024.png)](https://www.janestreet.com/puzzles/october-2024.png)

Pick **distinct positive integers** _A_, _B_, and _C_, and place them in the grid above. Your goal is to create two corner-to-corner trips — one from _a1_ to _f6_, and the other from _a6_ to _f1_ — both of which score **exactly 2024 points**.

A “trip” consists of knight’s moves. Squares may **not** be revisited within a trip.

The “score” for a trip is calculated as follows:

- Start with _A_ points.
- Every time you make a move:
    - if your move is between two _different_ integers, **multiply** your score by the value you are moving to;
    - otherwise, **increment** your score by the value you are moving to.

Can you find positive integers _A_, _B_, and _C_, as well as a pair of trips, that satisfy the criteria above? How low can you get _A_ + _B_ + _C_?

Please format your entry by concatenating your values for _A_, _B_, and _C_, followed by your _a1_-to-_f6_ tour, followed by your _a6_-to-_f1_ tour. For example, “1,2,253,a1,b3,c5,d3,f4,d5,f6,a6,c5,a4,b2,c4,d2,f1” would be a properly formatted entry.

To qualify for the leaderboard your value for _A_ + _B_ + _C_ must be **less than 50**.

Submitted: |   |   |   |   |   |   |
|---|---|---|---|---|---|
|N=12|0 8 1,5,2,a1,c2,d4,f3,d2,f1,e3,d1,f2,e4,f6,a6,c5,d3,e5,c4,d6,e4,c3,d5,e3,f1|||||