Can't the answer be 100? Since even though the criminals can't look behind them, they can talk to each other before they're lined up. They can pair up into groups and whisper to others what their color is and so when they're all lined up, they know their bandana color??

argh I like puzzles but I suck at them xD

a dark gray hexagon with + in it :3

puzzle 9? I think i did it right... red = 50 (Jeremy)

yellow = 75 (Elven)

orange = 100 - (Peter)

Pink = 125 (William)

My guesses

Puzzle 4 - is the answer 99? I think I seen this maths problem before where the answer was originally 75 but I remember a new solution being published that said it could be raised to 99 people! (Subeta time: 5.04)

EDIT: So if the first person counts an odd number of orange hats, and an even number of green hats, theyd say their hat was orange! or if theres an odd number of green they'd say its green! Then the next prisoner would work out how the amount of hats infront and after then if it was odd orange both ways (like 1 behind him and 49 in front) he'd say green. This would go on until the first prisoner who has a 50/50 chance cause they can't see any hats!

Puzzle 10 - 7/8 (Subeta time: 4.34)

Ooh, I also like puzzles but am not necessarily good at them. xD

Attempt for puzzle 10: 99/2 Looks like each shaded "set" is 1/2, and I think you might end up with 99 such sets?

Also, is it a correct assumption that green/orange are split 50/50 for puzzle 4?

Yup! Did you want a SP prize or WL item of your choice?

Yay! How much was the prize again? I'd love to get some cakes off my wishlist and/or MKBs if they fit the budget.

Also, text answer for puzzle 5: 1(LU 2x2), 2(LU 2x5), 3(LU 2x6), 4(LD 6x3), 5(LU 7x3), 6(RU 4x3), 7(6x1), 8(RU 2x3), 9(LU 2x4), 10(R 1x3). I can try to get my messy image in paint up if that's better, haha.

Gotta puzzle over the prisoner one some more.

2.2m in total (:c) (1.7+0.5) any combo of items.

solved for both nj~

it is irrelevant whether it is split 50-50. there's a convoluted answer in this thread already but it's incorrect because its imprecise. (the 2m is still up)

But! If there are n > 2 colors, up to 100 colors- how would you solve it? (if you solve this... hmm I'll give the prize of 50 CSC or 5m)

?

Those cakes work for me! :D

Well, if it's 100 colors, that would be easy if the people in front have increasingly good memories to remember what all the colors of all the other people before them were. ;p But I will probably have to sleep on this one!

Subeta time 12:40 - And the prompt suggests that there's no way to know if the person behind them had the right answer or not? (silent execution and silent...celebration/salvation?) And they don't know the total number of green vs. orange beforehand? (e.g. even if it's not 50/50, they also wouldn't know if it's like 25/75, 99/1, etc.?)

It's one long continuous line. They are bandana'd after lining up in any random distribution 1-99 33-67 anything.

(not in 3 columns)

They only see the colours in front relative to their position.

The executioner starts asking from the back of the line and moves up. They all can see the front but can't cannot see the back. They can hear the answers of the previous guys. They can only say 'orange' or 'green'

They all get to MEET UP before lining up and getting banada'd and having a meeting on how to make everyone survive and discuss their logic plan.

I know this is not going to the proper mathematical answer, but in their meetup for just these two colors, they could decide to pronounce orange/green differently depending on what color the person in front of them is, e.g. stress the first syllable for orange and the second syllable for green. So if the person in front of you is orange and you're guessing orange, you say OH-range to let the person immediately in front of you that they're orange, but if you say o-RANGE, it lets the person in front of you know that they're green. (Pronouncing green differently is a little tricky, but you could do it. Also if the guards aren't being mean and picky about pronunciation xD)

With this method, the first guy unfortunately has only a 50/50 shot of making it, but you could consistently save at least 99.

Oh, or wait, they could decide that orange means there's an even number of orange in front. If prisoner 2 still sees that there's an even number of orange in front, he knows he's green. If he sees an odd number of orange in front, he knows he's orange.

Attempt at formalization: G = Green O = Orange (I know you used A/B before but this reduces the number of variables I need to translate in my head xD)

X defined as even/odd status of number of orange previous person sees Y defined as even/odd status of number of orange current prisoner sees

If X = Y, prisoner says G If X =! Y, prisoner says O

Example: If the group decides that "orange/O" means even number of orange left GOOO P1 sees odd number of O, says G to let the group know there's an odd number of O left P2 sees even number of O, which is different from what the last person saw, so they know they must be O. They say O. P3 - P1 let them know there was originally an odd number of O, P2 also said O, which meant P2 saw an different (even) number of O. P3 sees an odd number of O ahead, which again is different from what the last person saw, so they must also be O. They say O. P4 - Based on all the O's, they know the odd/even pattern has been switching. Odd --> even --> odd. P4 sees an even number of O's ahead, which is different again, so they must also be O. They say O. They all live.

OOOO Same situation as above except P1 dies after letting the group know the pattern D:

GGGG P1 sees even number of O, says O to let the group know there's an even number of O left P2 also sees even number of O so they must not be O (i.e. they must be G) so they say G P3 - P1 let them know there's an even number of O left. P2 let them know this has not changed. They also see an even number of O in front of them (i.e. the same) so they know they must be G. They say G. P4 - Same logic as P3. They both see an even number of O in front of them. Everybody except P1 lives.

So it looks like you can consistently save at least 99 prisoners with a 2-color scheme.

With more colors, I think you'd have to sacrifice more people up front to let you know the odd/even status of each color. My guess is the number of people you can save becomes 100 - (number of colors - 1) although only up to a certain point (e.g. you could save everyone at 100 colors).

Yup. f(n) = Sum(n>n) -> odd | Sum(n>n) -> even for n = 0 f(n+1) = {q(x) = f(n) = f(n+1) -> (Odd OR Even)} AND not g(x); g(x) = {f(n) =/ f(n+1) -> (ODD or Even)} AND not q(x)

The more colours part is wrong however.

You can also use an upwards accent and a downwards accent to communicate a second piece of information (but that's not the mathematical answer).

This is such a fun idea!!! I'll take a stab at 'em.

Puzzle 8:

Across: 2. step 5. example 6. fire 7. invite ? 8. substance 11. quiet 14. scientific 15. day 16. genius 18. food 20. sordid 21. complete 22. letter ?? 25. thank(sgiving???)

Down:

1. juvenile
2. sisters
3. balk ??
4. devour
5. comparison
6. little
7. quip ?? quit??? idk
8. psychotic
9. passion
10. brother
11. sick
12. coherent
13. trend..(y???)
14. hall

This was harder than I thought lol, I couldn't really use the hints to help me when I was stuck since those were the ones I got more quickly!! I'm gonna go ahead and post this publicly, since I don't know if I want to put in extra time revising this and therefore don't care if people look at what I managed to come up with if they're working on solving it. I know SOME of them are right haha, so it might help a little.

It looks like Puzzle 4 was already answered, so I might play around with Puzzle 6 tomorrow if it hasn't been solved by then – it at least seems more straightforward.

very few wrong. most right. qx : here's another hint ritzy. qy : take a deep breath ... qz : lurking danger qw : amazon days prized cakes sent.

Across: 2. step 5. example 6. fire 7. invite 8. substance 11. quiet 14. scientific 15. day 16. genius 18. food 20. sordid 21. complete 22. 25. thank

Down:

1. juvenile
2. sisters
4. devour
5. comparison
6. little
8. psychotic
9. passion
10. brother
11. sick
12. coherent
14. hall

ahhhh thanks for taking pity on me, i know i didn't plan on revising my answers but i also can't just give up and let those clues sit there... some of them helped but i still feel like i'm missing something obvious! if these aren't correct, i hope someone else solves it soon so i can see the solution.

Across:

11. weigh
12. box (totally forgot this had to start with a B)
13. caroler ??? (i was going to guess it at first but there's too many letters, but the R and the E fit otherwise...)

Down: 3. halt? (idk why but short words are the hardest) 11. wary (i got the clues for 11 across and down mixed up, so at least i can guess words with the correct number of letters... but idk if my new answers are any more accurate) 23. ritzy