Mean, Median, and Mode
(Published on 27. May 2021, 00:00 by RockyRoer)
The Rules:
- Normal sudoku rules apply - fill every row, column and 3x3 box with the digits from 1 to 9, once each.
- From each circled cell, three arrows emerge. The circled cell represents the mean of the the digits on one arrow, the median of the digits on a different arrow, and the mode of the digits of the last arrow. You must determine which arrow is which.
The Puzzle:
Link for solving on f-puzzles:Be aware, because these arrows act differently than normal arrows, conflict highlighting has been turned off.
Statistics review:
- The arithmetic mean is the 'average' of the numbers - add them up and divide by the number of numbers.
- For 3, 4, 4, 9 the mean is 5.
- The median is the middle number when the numbers are sorted in ascending order -- or the average of the middle numbers if there is an even number of numbers.
- For 3, 4, 9 the median is 4.
- For 3, 4, 6, 9 the median is 5 (4+6 / 2)
- The mode is the most frequently occurring number. If there is a tie for the most common number, then both numbers are modes - but that wouldn't be allowed in this puzzle.
- For 3, 4, 9 there is no mode.
- For 3, 4, 4, 9 the mode is 4.
The Solution:
For those of you curious about the solution path, my solution is available here. Beware - obvious spoilers...https://tinyurl.com/zupeexe7
Solution code: The row that is the mode of the numbers 1, 1, 3, 9, followed by the column that is its median. (18 digits)
Comments
on 18. November 2021, 01:37 by mathpesto
Thanks so much for directly me to this puzzle after solving my mean/median/mode one! This was a good challenge but also a very clear way to tackle. Lots of fun!
on 29. June 2021, 18:04 by RockyRoer
Added link to solution path document for anyone curious. Beware of spoilers.
on 1. June 2021, 22:17 by ashwin
this was amazing
Reply: thanks for solving it! I’m so glad you enjoyed it!
on 31. May 2021, 08:10 by RJBlarmo
One of my favorite sudokus ever, with lots of unique logic and a beautiful ending. Had to restart several times but I finally caught my mistake and everything went smoothly after.
on 28. May 2021, 18:54 by RockyRoer
Fixed typo in German version of solution code. Sorry! Should need ROW 1 and column 2. Thanks @StefanSch for bringing that to my attention.
on 27. May 2021, 23:33 by marcmees
Very nice. Good logic.
on 27. May 2021, 23:28 by henter
Very interesting puzzle!
REPLY: Glad you enjoyed it! Thanks for solving!
on 27. May 2021, 11:43 by henrypijames
What an original concept! Another instance of "How the heck can this puzzle exist?"
As someone who loved stochastics and hated statistics back in school, I feel compelled to do this puzzle.
BTW, "For 3, 4, 9 there is no mode" is not correct - all three are mode of that series, but there is no *unique* mode.
REPLY: I hope you do try it! Anyone of these rules for arrows brings some interesting new logic to the table -- and this one add's all of them -- so there's a lot of cool new things to discover. It's got a very logical and tight solution path with small deductions along the way as you determine what type of average each arrow is, and therefore what that means for the rest of the puzzle. Good luck! Feel free to hit me up with a hidden comment, or on CTC discord server if you need any advice.
