Brainsteem #8 Prize Maths Puzzle [Win 2SBD+1SBD]
Remember that there are TWO prizes to aim for.
Calculate the average value of the expression
(a - b)2 + (b – c)2 + (c – d)2 + (d – e)2 + (e – f)2
over all possible arrangements of (a, b, c, d, e, f) of the six numbers 2, 3, 5, 12, 15, 16.
On the face of it, this seems like a long hard slog of enumerating 6! = 720 different arrangements of the six numbers. However, there is a shortcut!
Prizes
To qualify you must upvote this post and write the answer in a comment.
To win First Prize you must include the answer and a valid method.
The First Prize will be 2 SBD or the chance of a @randowhale upvote.
The Second Prize will be 1 SBD to any other correct answer in the comments section, chosen at random.
Prizes will be awarded after the 7 days have expired. Winners will be announced at the next puzzle after the draw.
The main thing is to enjoy the challenge and maybe learn something new.
Come and check out other challenges currently live!
Science Cryptic Crossword SCX1 [Win 10 SBD Prize]
Brainsteem #7 Prize Maths Puzzle [Win 2SBD+1SBD]
Brainsteem #6 Prize Maths Puzzle [Win 2SBD+1SBD]
Brainsteem #5 Prize Maths Puzzle [Win 2SBD+1SBD]
And don't forget to upvote each other's comments to bring cheer to the whole community!
Expanding (a - b)2 + (b – c)2 + (c – d)2 + (d – e)2 + (e – f)2, we have a2+2b2+2c2+2d2+2e2+f2-2(ab+bc+cd+de+ef).
If we consider the average, then each of these square terms should have the same average: 110.5
Each of the consecutive letters should have the same average: 1073/15
So average of the original expression should be 10 (110.5) - 2(5*1073/15) = 1169/3
Hi, as the only other correct answer, you win the random 2nd prize with a probability of 1!
Well done!
Thanks man, this one is a really interesting question!
Hi @kenchung, thanks.
BTW have you seen this article of mine?
https://steemit.com/steemdev/@rycharde/automatic-related-posts-engine-in-article-footer-development-concept-devs-wanted
Any ideas?
yup I saw it and I really like your article! Really need to have this feature.
I know turnout for this question was rather disappointing. However, I am curious since the only answers offered were the same... so, are @kenchung and I both correct or both wrong?
Hi, apologies for taking a while to reply - been very busy.
Yes, both of you correct, even if slightly different method. As you were first you win the 2SBD :-)
Congratulations!