:: Code breakers ::

Mastermind (Code breaker), a game where there are 4 slots to be filled with 4/5 colours... & given with only limited tries to solve the hidden code.

well, i used to play codebreaker of neopets when i was still a teen... & somehow came up with a simple way to tackle it...
recently, I'm been playing guild party quest of maple story (SEA) of stage 3... where r 4 slots with 4 items (food, wine, scroll & badge)...
whichever the case is this is still code breaker...

before we start in to my proposed approach, let's look into the max. no. of possibility of we play around with the no. of slots (x) and no. of objects (y). the layout will be quite similar to a graph for the ease of adaptability.
5----5--25--125--625 ----- lazy to count liao... :X
4----4--16---64--256--512
3----3---9---27---81---243
2----2---4----8---16----32
1----1---1-----1---1------1
y/x--1---2----3---4------5

if you still can recall your upper secondary elementary mathematics (sec 5 for me), we ben taught how to find the equation for this series of number... pls take a moment to think thru, else juz scroll down for the answer...

Max(number of slots, number of objects)
Max(x,y) = y to the power of x, y^x

for maplers,
max(2,5) = 25 ( it is somehow kerning party quest stage 2... with a attached condition, 2 of the slots must be object 1 and 3 slots must be object 2. hence, the actual no. of possibility will be less than 25.)
max(2,6) = 36 (kerning party quest stage 3... 3 slots must be object 1 and the other 3 is object 2)
max(2,8) = 64 (lubridum party quest stage 8... 5 slots must be object 1 and 3 slots is object 2)
to solve the above type of code breakers, just do a simple trial and error...
eg: max(2,5)... object 1 = 1, object 2 = 0
start with 11100, 11010, 11001, 10110, 10101, 10011, 01110, 01101, 01011, 00111... & stage clear... so that number of possibilities been reduced to 10 instead of 25... thanks to the attached condition...

max(5,3) = 243 (similar to orbis party quest... thankfully there is another rule to ease the solving process; sum of 3 slots is equal to 5...
to solve this code breaker, you can draw out a flowchart or if u r familiar with programming, u can use a logic run... i have place the flowchart in words format... sry, if it looks too messy to you.
start with 500 (note: 5+0+0 = 5)
3 possible conditions; clear, 1 correct or all wrong...
I) if 1 correct, it cant be the 5 which is correct...so either slot 2 or slot 3 is correct...
so the next step will be 410, this is to test whether the 3rd slot is 0 or not...
once again 3 possible results will be given; clear, 1 correct or all wrong...

Ia) 1 correct,
assuming the 3rd slot is still 0... so try 320,
if result is 1 correct, then run 230, 140 and 050.
if result is all wrong, then 3rd slot is not 0. the answer is 401. (rmb 410 gives 1 correct, so 1st slot has to be 4 and 2nd slot is 0.)

Ib) all wrong, then the 2nd slot should be 0, so run the following sequence till stage clear; 302, 203, 104 and 005.

II) if all wrong, then next try will be 311 ( note:3+1+1=5)
3 possible conditions; clear, 1 correct or all wrong...

IIa) 1 correct, so either the 2nd or 3rd slot has to be 1... try 221
3 possible conditions; clear, 1 correct or all wrong...

IIa1)1 correct, try 131
assuming the 3rd slot is still 1... so try 131,
if result is 1 correct, then run 041.
if result is all wrong, then 3rd slot is not 1. the answer is 213. (rmb 221 gives 1 correct and 2nd slot is 1.)

IIa2)all wrong, so 2nd slot is 1... try 113 & 014...

IIb) all wrong, try 122
2 possible conditions; clear or 1 correct...
IIb1)1 correct, try 032 and 023

Ok enough of mastermind similar code breakers... here is the one which is totally similar to mastermind except dat, the number of objects and tries is less than mastermind.
Guild party quest in perion....
Max(4,4)=256 with only 7 tries...

to be continue...

if you wan an alternative approach...
http://www.tnelson.demon.co.uk/mastermind/

of coz, there are also other options... juz do a simple net search & various ways of solving mastermind will be available...

+ BL updated @ 5:12 AM

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