Every Saturday at Netopia's Square, a peninsula at the tip of southwest Netopia, there is a leaderboard kept of Netopia's Square's six local resident wizards.

(in no particular order)

They are ranked based on the their acts of magic for the previous six days.

The highest ranking is 1 and the lowest is 6.

The leaderboard displayed on the Saturday before last listed Javacodia as the highest because he had cast a spell that defeated a nasty virus threatening to wipe out the village.

The others were:

2. Pythono

3. Ceeplis

4. EsquEll

5. Mykro

6. Fortran

Last Leaderboard Last Saturday's leaderboard rankings had each wizard ranked in a different position from the previous Saturday.

Magic Stats

1. Pythono's change in ranking was the greatest of the six.

2. The product of EsquEll's rankings for the two weeks was the same as the product of Fortran's ranking for the two weeks.

## What were the new rankings on the Magic LeaderBoard?

Notice that

Fortran is ranked 6 and EsquEll is ranked 4. So, for 2) to be true, we must find two rankings such that 6 * a = 4 * b. Only (2,3) or (4,6) for (a,b) are possible. But suppose Fortran was ranked 2 the previous week and EsquEll was ranked 3. Then Fortran would have fallen 4 slots, but Pythono, in rank 2 the second week, would have risen a maximum of 4 slots. Thus this violates 1) and the second possibility is the correct one. Thus, Fortran would have been in fourth place the previous week, and EsquEll would have been in sixth the previous week. Now, we have Mykro, Javacodia, Ceeplis, and Pythono left to place. Because Pythono's ranking changed the most out of the group, place him in fifth, so he rises three slots and gives us the most wiggle room. Now, in order to avoid violating 1), we place Mykro in third the previous week, so he falls two slots between weeks. Finally, we put Ceeplis in first and Javacodia in second to avoid violating the condition that each wizard's ranking changed from the first week to the second week.
Final leaderboard for the Saturday before last:
1. Ceeplis
2. Javacodia
3. Mykro
4. Fortran
5. Pythono
6. EsquEll

• Is there a way for me to post a spoiler comment, so that I may contribute or discuss the puzzle more in depth without ruining it for future puzzlers? Apr 11 '20 at 20:07
• @JohnS. encrypt it as rot13.com Apr 11 '20 at 20:49
• @Cloudy7 - Your use of 'rise' and 'fall' seems backwards, given that the puzzle states that 1 is the highest rank. Apr 17 '20 at 0:53
• @LannyStrack The puzzle asks to find the leaderboard two weeks before the given day, not the leaderboard on the given day. Apr 17 '20 at 0:58
• @Cloudy - No, it doesn't. The rankings that are given are from the "Saturday before last", and the puzzle asks you to provide the "new rankings" for a week later (last Saturday). Note the question in bold at the end. Apr 17 '20 at 1:02