PROBLEM LINK:Author: Anudeep Nekkanti DIFFICULTY:CAKEWALK PREREQUISITES:ADHOC PROBLEM:Given a circle, you can make cuts at positive integered angles intersecting at origin. You are given 3 type of questions to answer.
QUICK EXPLANATION
EXPLANATION
Strategy of making distinct angles: Complexity: O(1). All we need to do is constant number of multiplications and divisions. Hence time complexity is constant or O(1). AUTHOR'S, TESTER'S AND EDITORIALIST's SOLUTIONS:Author's solution
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asked 19 May '14, 00:23

Well, that was frustrating... The statements:
Are ambiguous. It gives the idea you should use the WHOLE cake. The examples worked when thinking that way. answered 19 May '14, 00:48
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Yes. The whole cake has to be used. (Why waste it?) For N=3, you are thinking of taking sectors 90, 90, 90 and throw the remaining 90. But this will result into cutting into 4 pieces.
(19 May '14, 00:56)
Ohhh, now I get it. Sorry, that was dumb...
(19 May '14, 01:00)
n*(n+1)/2?you have written that the pieces will have angles 1,2,3,..n. for example to cut in 4 pieces with the third condition,angles should be 88,89,91,92 and not 1,2,3,4 as they do not cover the whole cake?
(19 May '14, 01:20)
@ashish424 you need to think carefuly let for example n=2(even)then angles will be 179 and 181 as 360/2=180 and 2/2=1 so 1801=179,180+1=181 for n=3 (odd)will be 119,120,121 as 360/3=120 and so u have 3's 120 so add 1 to one 120 and subtract from other for n=4 (even) n=2(even) then angles will be 179 and 181 as 360/4=90 and 4/2=2 so (902,901)and (90+1,90+2).try to do for n=5,6,7.. you will get it now suppose for n=10(even) then angles will be (365,364,363,..,361)and (36+1,36+2,..36+5)here 360/10=36 and 10/2=5 so add (5,4,.,1,.,5{0}(xcept zero)go on try for n=26 and 27 u will get it
(19 May '14, 01:49)
add(5,4,.,1,.,5{0}(xcept zero) is zero for any case sorry still doesnt get it
(19 May '14, 02:18)
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@ashish424: You can make angles starting from 1, 2, 3 like this. If you have to make n pieces and you have already made n  1 cuts, the remaining angle itself will be greater than n  1. Hence in this way all the angles will be distinct if n * (n + 1) / 2 <= 360'.
(19 May '14, 07:23)
@ashish424: I have edited the editorial accordingly.
(19 May '14, 07:26)
add {365,364,363,..,361,36+1,36+2,..36+5)
(19 May '14, 08:50)
continuing n=10(even) then angles will be (365,364,363,..,361)and (36+1,36+2,..36+5)here 360/10=36 and 10/2=5 so add (5,4,..,1,2,...,5{0} to (360/10=36 )(xcept zero)u will get angles like 365=31,364=32,...,31 and then 36+1=37,36+2=38,...,36+5=41... and try for doing n=26 and n=27 ... you will get the extreme cases for which the question "Is it possible to make N pieces, such that no two of them are equal?" satisfied ... still not understood .. feel free to ask ..
(19 May '14, 11:32)
got it Thanks!
(19 May '14, 16:43)
@sanzzzay you have explained the division of n cuts of n which divides 360.What if n doesn't divide 360 ?How will you make the division then?
(19 May '14, 17:29)
@lalit_horcrux lets take n=5(odd) then 360/5=72 then 722,721,72,72+1,72+2 taking 72 as mean.. then n=7 ok then (360/7=51.42 )and let take 51.42 as 51 then {513,512,511,51,51+1,51+2,51+3} adding these makes 357 so takes the last one 57 ... the above explanation is just the another approach to solve the "Is it possible to make exactly N pieces from the whole cake, in such a way that no two of them are equal?" you can say it is hit and trial method ... try doing n=26 and n=27 you will get the answer ..
(19 May '14, 22:22)
@ashish424 did you get my explanation ...?
(19 May '14, 22:23)
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Can anyone help me which constraint i misleading? My solution: http://www.codechef.com/viewsolution/4119374 answered 20 Jun '14, 18:33
if(n!=2  n>26) { printf("y\n"); } else { printf("n\n"); Hi @tech_boy please can you explain why you give the above condition thankx
(20 Jul '14, 19:32)

Just a quick illustration: if you want to make 26 different slices you would go from 1, 2 ... 25 which equals 325 and the last slice would be 35. You could also try 27, but 1, 2, .. 26 equals 351  and the last slice would have to be 9 (repeating itself). So 26 is the limit. answered 27 Jul '17, 12:27

I made the 3rd part <=25 instead of <=26. hence wrong ans
I wish to know that why is prerequisite marked as adhoc for cakewalk questions.
@yash_15, The problem does not belong to any specific category, it needs some simple observations, So the most suitable category for it is adhoc.
For n=2 If we divide,the cake in 2 pieces then in the third part compulsory both the angles will not be 180 degree?
The Ac solution gives y y y for n == 1 but for n = 1 that is for no cuts, we can't get either equal or unequal piece. Will someone explains what I am missing.