Who Stole The Cookie?

i will call them M,R and N for short . i divide this problem into 3 posibilities

• if M took the cookie.M speaks the truth => FALSE . if M lies => 1 of the other 2 must speak the truth which is just a possibility since that person can be R,not always true => M COULD HAVE TAKEN COOKIE.

• N took cookie.N speaks the truth => FALSE .if N lies => 1 of the other 2 must speak the truth which is just a possibility since that person can be R too => not always true => N COULD HAVE TAKEN COOKIE.

• R took cookie.R speaks the truth => TRUE . if R lies => FALSE => R CAN'T HAVE TAKEN COOKIE. problem solved :d

Statement 1 and 3 cannot be FALSE at the same time. Any one of them must be true. So statement 2 is false since there is only one child speaks truth

I solved the problem by visualizing the situation. I took note that there were three kids: Marsha says = Nicky stole it Rob says = I stole it Nicky says = I didn't steal it Basically, I remembered a fact about kids and it's that they have underdeveloped conscience and will not have an advanced understanding on moral judgments of what's right and what's wrong. Here's the thing: Marsha blames Nicky, which is typical for a kid to do to avoid punishment. Then Nicky denies that statement, again which is typical for a kid to do to avoid a spanking or berating. However, Rob has claimed he stole the cookie which is highly unusual for a child to do. He could've lied or remained quiet but no. So I based analysis 1 on a psychological perspective. Analysis 2, would be more of arranging everything in order. So marsha says nicky stole the cookie, we go to nicky. Though, nicky claims she did not steal it. Notice that Rob was not mentioned in their arguments. Then all of a sudden, he admits he stole the cookie. Magical huh? So it's kind of like this: Marsha => Nicky, ?Rob?

(A) Who is telling the truth (B) Elimination of choices Case 1 (A) If Marsha = true then Rob = false Nicky = false Case 2 (A) If Rob = true then Marsha = false Nicky = true 'if two of them is telling the truth then 'this case 2 = false (void) 'GIVEN = ONLY ONE OF THE THREE KIDS IS TELLING THE TRUTH 'this case is a VOID Case 3 (A) If Nicky = true then Marsha = false Rob = true/false == > FALSE The given is (Nicky = true) therefore stating (Rob = false) Case 1 (B) If marsha = true then marsha didn't steal cookie rob didn't steal cookie Nicky stole the cookie Case 2 (B) = VOIDED Case 3 (B) If nicky = true then Marsha could have stolen the cookie Rob didn't steal the cookie Nicky didn't steal the cookie Rob didn't steal the cookie = true in all statements answer = Rob didn't steal the cookie. My god!! It took me almost an hour to finally get the answer!!

If Rob is telling the truth then Nicky must also be telling the truth, which violates the given that only 1 child can be telling the truth. If Rob is lying, then he didn't steal the cookie. Therefore, Rob could not have stolen the cookie in any possible solution.

Case 1: If Nicky stole the cookie, Marsha is telling the truth. Rob and Nicky are lying=> Rob did not steal the cookie

Case 2: If Marsha stole the cookie, Nicky is telling the truth. Marsha and Rob are lying=> Rob did not steal the cookie.

Case 3: If Rob stole the cookie, both Rob and Nicky are telling the truth which invalidates the given condition that only one of them is telling the truth.=> Rob did not steal the cookie.

Verdict: ROB COULD NOT HAVE STOLEN THE COOKIE.

Mind Flow Chart:

1. Marsha 's and Nicky 's statement cannot be both true(or false).

2. One of them must be telling the truth.

3. Given that only one children is telling the truth.

4. Rob must be lying.

5. He did not steal the missing cookie .

Lets denote $M$ (resp. $R$ & $N$ ) the Boolean that is true if Marsha (resp. Rob & Nicky) stole the cookie.

• Marsha says that Nicky stole the cookie: If it's the truth: $N$ holds. If it's a lie: $(R+M)$ holds.
• Rob says that he stole the cookie: If it's the truth: $R$ holds. If it's a lie: $(M+N)$ holds.
• Nicky says that she didn't steal the cookie: If it's the truth: $(R+M)$ holds. If it's a lie: $N$ holds.

Since only one of them can tell the truth at once, we have:

• If Marsha tells the truth, then $N\times (M+N)\times N$ holds.
• If Rob tells the truth, then $(R+M)\times R\times N$ holds.
• If Nicky tells the truth, then $(R+M)\times (M+N)\times (R+M)$ holds.

Thus, after simplification (all the byproducts being false):

• If Marsha tells the truth, $N$ holds.
• If Rob tells the truth, $0$ holds. ( Impossible )
• If Nicky tells the truth, $M$ holds.

Three conclusions can arise from these results:

1. In none of these cases does $R$ hold, so Rob cannot be the thief.
2. However, Marsha and Nicky are potentially the culprits depending on whoever is telling the truth.
3. Rob cannot be telling the truth since it would result in an impossible statement. (He's apparently protecting one of the other two)

Three cases we need to consider here. Since only one of them is telling the truth, it boils down to (True, False, False), (False, True, False), (False, False, True)

Case 1 : - Marsha is telling the truth, Rob and Nicky are lying => Nicky stole it, Rob didn't steal it and Nicky stole it => Nicky stole in this case

Case 2 : - Marsha and Nicky are lying, Rob is telling the truth => Nicky didn't steal it, Rob stole it and Nicky stole it ... Since two person couldn't have stolen the cookie, this case is invalid

Case 3: - Marsha and Rob are lying, Nicky is telling the truth => Nicky didn't steal it, Rob didn't steal it and Nicky didn't steal it => Marsha stole the cookie in this case

So out of the three possibilities Marsha and Nicky could have stolen the cookie, but never Rob. The answer should be "Rob didn't steal the cookie"

One of Marsha and Nicky told the sole truth (from "only one of the three kids is telling the truth"), so Robert must have lied in his admission of guilt. Robert is definitely innocent.

Marsha and Nicky were telling opposite things. One of them is telling the truth while the others lies. => Rob lies. He didn't steal it