13 Coins Solution

Thought of the day: On the trip up, we saw a Transformer decal and we were wondering if it was the Autobots or Decepticons. This led to an interesting point. Does to deceive mean to lie? I personally think they’re different. If i had lied to someone, it doesn’t entail that the person believed me. But if I had deceived someone, that means at some point in time, that person was tricked. Lets use another sentence. “I deceived person x.” vs “I lied to person x.” Although both are valid sentences, they are clearly different in meanings. Personally, the 1st one sorta means, I had lied to person x and he believes in my lie, while the 2nd sentence means I had lied to person x, but doesn’t necessarily mean he believed in the lie. So all I’m trying to say is that lying is an action while deceive refers to the state after lying. Sorta like saying you can always fail at deceiving, but you can’t fail at lying.

Here are the answers to yesterday’s riddles. If you want to try it before reading the solution, I would highly suggest you read yesterday’s entry before reading the solution.

9 coins:

• randomly chose 6 coins and weigh 3 on each side (weigh #1)
• if scale is balanced:
  • that means the heavier coin is in the remaining pile
  • choose 2 coins from the remaining 3 and weigh 1 on each side (weigh #2)
  • if scale is balanced, unweighed coin is the counterfeit
  • if scale is unbalanced, the heavier coin is the counterfeit (u were told the counterfeit was heavier)
• if the scale is unbalanced:
  • chose the pile which is heavier (since counterfeit is heavier, making the total weight of the 3 coins the counterfeit is in heavier than 3 real coins)
  • choose 2 coins from that pile of 3 and weigh 1 on each side (weigh #2)
  • if scale is balanced, unweighed coin is the counterfeit
  • if scale is unbalanced, the heavier coin is the counterfeit (u were told the counterfeit was heavier)

13 coins:

• randomly choose 8 coins and weigh 4 on each side (weigh #1)
• if scale is balanced:
  • label the remaining 5 coins: I, J, K, L, M
  • label one of the original 8 coins in the 1st weigh A (we know A is real since there’s only 1 counterfeit)
  • weigh I + J against K + A (weight #2)
  • if scale is balanced:
    • you know L or M is the counterfeit
    • weigh L against A (weigh #3)
    • if scale is balanced, M is the counterfeit
    • if scale is unbalanced, L is the counterfeit
  • if I + J is lighter than K + A:
    • you know either I, J, or K is the counterfeit
    • if I or J is the counterfeit, that means the counterfeit is lighter than the real
    • if K is the counterfeit, that means the counterfeit is heavier than the real
    • weigh I against J (weigh #3)
    • if scale is balanced, K is the counterfeit
    • if scale is unbalanced, the lighter of the 2 coins (I or J) is the counterfeit (since we already proven that the counterfeit is lighter if I or J is the counterfeit)
  • if I + J is heavier than K + A:
    • you know either I, J, or K is the counterfeit
    • if I or J is the counterfeit, that means the counterfeit is heavier than the real
    • if K is the counterfeit, that means the counterfeit is lighter than the real
    • weigh I against J (weigh #3)
    • if scale is balanced, K is the counterfeit
    • if scale is unbalanced, the heavier of the 2 coins (I or J) is the counterfeit (since we already proven that the counterfeit is heavier if I or J is the counterfeit)
• if scale is unbalanced:
  • label the coins on the lighter side as A, B, C, D and the coins on the heavier side as E, F, G, H
  • label one of the remaining coins that weren’t weighed as I (I is guaranteed to be real since the counterfeit must be in the 8 coins that were weighed)
  • if A, B, C, or D is the counterfeit (then the counterfeit is lighter than the real)
  • if E, F, G, or H is the counterfeit (then the counterfeit is heavier than the real)
  • weigh A + B + E against C + F + I (weigh #2)
  • if scale is balanced:
    • either D, G, or H is the counterfeit
    • if D is the counterfeit, then the counterfeit is lighter than the real
    • if G or H is the counterfeit, then the counterfeit is heavier than the real
    • weigh G against H (weigh #3)
    • if scale is balanced, D is the counterfeit
    • if scale is unbalanced, the heavier coin is the counterfeit
  • if A + B + E is heavier than C + F + I:
    • given the conditions above, A, B, F, and I are real (since A and B have to be lighter to be counterfeit and F has to be heavier to be the counterfeit; I has always been real since the 1st weigh)
    • that leaves only C or E to be the counterfeit
    • weigh C against I (weigh #3)
    • if scale is balanced, E is the counterfeit (since C no longer is)
    • if scale is unbalanced, C is the counterfeit
  • if A + B + E is lighter than C + F + I:
    • given the conditions above, C, E, and I are real (since C has to be lighter to be the counterfeit and E has to be heavier to be the counterfeit; I has always been real since the 1st weigh)
    • that leaves only A, B or F to be the counterfeit
    • if A or B is the counterfeit (then the counterfeit is lighter than the real; copied from above)
    • if F is the counterfeit (then the counterfeit is heavier than the real; copied from above)
    • weigh A against B (weigh #3)
    • if scale is balanced, F is the counterfeit (since A or B no longer is)
    • if scale is unbalanced, the lighter coin is the counterfeit (since A or B is the counterfeit)
• right now, we can only find the counterfeit with 13 coins. with 12 coins, you can find the counterfeit and be able to tell if it’s heavier or lighter. i think the original puzzle was 12 coins, but i think the more coins the better the challenge. hehe

check out what zultimaz got @ frank and sons: FMA. full metal alchemist figurines.

got this link from /. : sex bots. in this article we’ll be exploring robot love. i made a couple of simple lego mindstorms robots and programmed them to reproduce — i.e. they can swap code. effectively, two robots come together, trade their genome, die, and two new robots are born in their place.

got this article from /. : Fahrenheit FBI – VoIP Wiretapping. The Federal Communications Commission voted 5-0 last week to prohibit businesses from offering broadband or Internet phone service unless they provide police with backdoors for wiretapping access. Formal regulations are expected by early next year. … In the police agencies’ original request, submitted in March, they asked the FCC to force surveillance back doors into instant-messaging programs and voice over Internet Protocol (VoIP) applications that do not use the traditional telephone network. The FCC politely declined, with Chairman Michael Powell saying those services were exempt from the Communications Assistance for Law Enforcement Act (CALEA) and that it was “unnecessary to identify future services and entities subject to” mandatory wiretapping requirements.

got this link from /. : Cell Phone with Built-in Projector. other similar products include: VKB and Canesta Keyboard. so reminds me of final fantasy – the spirits within when their whole control panel was a big hologram.