SOME SUM? - Must click the Flag to start. The problem/puzzle is explained on the Stage. Click a Red button to place that Number in a Cell. Click a Purple Circle to select the Cell to put it in. Click (Reset) to reset the whole puzzle. You can't select a number already in another Cell ! This can prove an issue if you want to put a number already in a Cell, somewhere else, or swap 2 numbers. You'll need to Clear it (blank Red button) first (or one of the 2 if swapping) so you can select it to go elsewhere, or just click (Reset) to start again. December 2023 Update: The Cloud Variable "Solved" still does its thing recording which of the 2 distinct solutions you found (if you solved it). However since we can no longer {See Data) for the Cloud it's pretty useless, so I have now added a Cloud List which will record the first 48 Scratchers to solve the puzzle (either solution). I have initialised it with those who I know, from when I could see Cloud Data, have already solved it. Hopefully you can get on the List too. The Scratchers who solved it before I added the Cloud List (& which solution they found), were: 1 - me (1 & 2) 2 - @colinmacc (1 & 2) 3 - @PutneyCat (1 & 2) 4 - @gor-dee (1 & 2) 5 - @kc021 (?) 6 - @mrabdul (1 & 2) 7 - @-Heron- (1 & 2) 8 - @MinecraftCoder17 (2) 9 - @TheGamer9999999999 (2) If you liked this puzzle, I made a similar (but considerably easier) one called Some Sum 2 - https://scratch.mit.edu/projects/972257364/ that might like to have a crack at. Enjoy! Regards Greg
Created by @gregatku for use in Coding Classes for Kids Unlimited, for whom I work as a Coding teacher. This is a problem/puzzle posed to me by a student in my Maths Problem Solving class at Wheeler's Hill Primary School. We were unable to solve it in class. I later solved it and figured it would make a great Scratch project so here it is. My student called it the Some Sum problem. Not sure why, maybe because "some" of the numbers "sum" to the same total, or maybe because it is indeed some Sum? Anyway I thought it was a pretty cool name so I stuck with it. It is non-trivial to solve. I have found 2 essentially different sets of solutions. Each of the 2 sets can be derived from the other. There are 6 solutions in each set being reflections and rotations of each other. I'm not certain if there are any others, but I very much doubt it. The interesting additional facts about this puzzle, that are only revealed when you solve the puzzle, are courtesy of the astute observational skills of @gor-dee. Thanks also to @grandpasp for the (Reset) button suggestion. If you do find a solution, see if you can find another solution from the other set of 6 solutions. The 2 Sets of Solutions each have different Red & Blue Sums. The most interesting aspect of this problem (to me at least), is that 2 of the smartest Mathematicians I know, each gave up after spending over 4 hours trying to solve it mathematically. But using systematic trial & error (which I did on paper in 90 minutes, before creating this project), the problem isn't too difficult, and it is much easier and quicker to do that sort of trial & error using this project. Have fun trying to solve it. Oh and don't think will you get any clues from Seeing Inside at the Code. The Code does not know any solutions. It only knows when you've solved it, the same way you do. @kc021 calculated that there were 3628800 possible permutations. And @mrabdul wrote a brute force Python program to try all those permutations, the results of which showed that there were indeed, 6 solutions in each of 2 sets of truly unique solutions.
