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araver

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Posts posted by araver

  1. 30 minutes ago, Thalia said:

     

    1.Do Germany and Australia's saves show in the night post if their target wasn't targeted for a kill?

    2.If Germany's save backfires, are we told?

    1. No.

    2. No.

  2. Night 1: Once more unto the breach. Once more?

    ~~~~~

    Seven people awoke at the same time to find themselves in a dimly lit room. A round doughnut table with chairs was in the center of the room. Most of them were dressed informally and as they surveyed their surroundings some tried to remember where there were the previous day. Yeah, everybody pretty much wanted an explanation for their presence there. Some had heard rumors of experiments in previous years and some had witnessed them but memories were fickle at best. And most had refused to believe something like this could happen to them (again). As rumors were passed in whispers from one another the chatter increased across the room.

    A flash and a hooded figure appeared in a mist in the center of the round table, surrounded by a cone of light.

    "If you can have a seat, I'm sure we can find a way to answer your questions as quick as possible. Some of you might already know where I'm going with this ... but I'm afraid that lessons were not learned, so he we are again.", they heard from the figure. One by one they moved towards the table, eyes cast on the figure.

    "Sometime ago, after being fed up with your reckless messing with forces beyond your control, I've attempted to ... mend the ends so to speak. While it worked for a little while, the situation has taken a turn for the worse recently and I find myself again unable to stand idly and watch. So hear me out!".

    "You are playing for your lives and your nations interests as well. Out of this room, you'll find color coded rooms. Don't mind the empty rooms. Inside your room you will each find a safe that only opens with your fingerprints and iris scans. Inside the safe an envelope with instructions. Study them wisely and remember time is scarce. Also, nothing exists outside of these rooms unless I tell you. We’ll adjourn in the morning!"

    The Hooded Figure disappeared without a sound and the doors squeaked open by themselves. One by one, they retreated to find their quarters.

    ~~~~~

    The Secret Alliance member was watching his target from across the bar. As he watched his target order another round of drinks he sighed. "Yet another Bond". He left the bar twenty seconds after his target and walked towards faking a dizzy step along the way. As Plasmid stopped at his door and glanced over the shoulder, all he saw was someone trying to find balance. Key in door, he heard the blip from the door opening followed by the crush of a body against the floor. "Are you OK buddy?" he asked turning around slowly ... but as his eyes began to take in the sight he felt a tingling in his neck. As his hand tried to reach up towards the place his brain wanted investigated, his own brain played a trick on him. It surely wasn't that big of a ... he fought to finish that thread of thought as he collapsed to the floor, caught by hands that muffled the sound. His body was not to be found till morning.

    ~~~~~

    The Swede had studied all the things the Hooded Figure had provided him with and pondered his odds. He had to be subtle about it, cause no one actually wants peace with both arms open. He went off the corridors and to the fifth room on the corridor. Cautiously he sprayed the content of one of the vials in his toolkit to the doorknobs and heard a small puff as the metal liquified. Maurice won't be joining tomorrow's talks. Except via Skype but that wasn't counting as present nowadays.

    ~~~~~

    Tl;dr version:

    Spoiler

    * China invades Plasmid's
    * Sweden quarantines maurice

    ~~~~~

    Players:

    1. Thalia
    2. bonanova
    3. Molly Mae
    4. Flamebirde
    5. maurice - quarantined by Sweden
    6. MikeD


    7. plasmid - Invaded N1 by China

    Day 1 ends Wednesday Feb 22nd at 9 PM UTC (About UTC). That means 4 PM EST and 11 PM for me.

    • Upvote 1
  3. 1 hour ago, flamebirde said:

    So if Sweden messes up the RID kill (i.e. misidentifies the target), can Sweden try again? That is, is the RID kill "one success per game" or "one attempt per game"? And if Sweden does misidentify the target, are we notified?

    One attempt per game.

    No, only succesful RID kills appear.

  4. Adding the FAQ from the signup thread:

    1. The OOA seems to say that the NK will happen before anything else. How does that work with saying it can be saved from? 

    That's why there's a separate rule saying save protects from NK. Other than this loop, the OOA is linear from left to right.

    2. Just to be sure, does save refer only to protect or to the save part of the trap as well? 

    Both of them.

  5. 7 minutes ago, Thalia said:

    HOST: The OOA seems to say that the NK will happen before anything else. How does that work with saying it can be saved from? 

    That's why there's a separate rule saying save protects from NK. Other than this loop, the OOA is linear from left to right.

    7 minutes ago, Thalia said:

    HOST: The OOA seems to say that the NK will happen before anything else. How does that work with saying it can be saved from? 

    That's why there's a separate rule saying save protects from NK. Other than this loop, the OOA is linear from left to right.

  6. UN Mafia III

    Secret Alliance: Wincon - Last standing
    China -- The size of the country allowed it to send a replacement for the representative lost in the previous game. Each night chooses a player to target and remove from the game. Action is unstoppable except via save. Will use its electronic interception technologies to find out the identity of the target if target is saved. Once during the game (ODTG) can remove a vote.

    UN Alliance: Wincon - Last standing.
    USA -- The size of the nation and its offensive capabilities, demand it acts but not two nights in a row. Chooses to invade (kill) on even or odd nights at the beginning of the game. Must invade on said night, if no target is drawn it is randomly selected (cannot invade self).

    Germany -- Its economic influence grows steadily which leads to an increase in political influence. Sometimes is forced to save nations in dire need, but would prefer preventing actions. Each night can save a player but there's a 50% chance that this backfires in which case Germany loses its vote the next day.

    Russia -- Has hundreds of satellites floating in space. Can use one per night to spy an alive nation either to see who targeted it or to see who that nation acted upon. Once during the game (ODTG) Russia can instead get lucky and find out a player's true role.

    United Kingdom -- Has worldwide influence among its former colonies. Once per night it can blockade a country, but not the same country twice in a row. Blockading stops any day or night action except for ODTG actions and the Secret Alliance's night invasion.

    Australia -- Has an interesting choice of possibilities due to its cultural diversity. Has 4 agents at its disposal, each can be used once: 1. Add 1 extra secret vote, 2. Remove a vote, 3. Protect (save but cannot be cast on self), 4. Break quarantine (used during the day can make the player quarantined by Sweden able to vote and be voted for).

    Indy
    Sweden -- A nation with nothing to contribute to war and naturally inclined to peace. From time to time, may choose to temporarily side with a Faction or the other, in order to protect its own interests. Each night can quarantine a country but not the same twice in a row. Quarantine acts like a trap - saves from kills / invasions and renders the target neutral - unable to vote the next day or be voted for (but can speak). Once during the game (ODTG) can veto out a country (RID Kill) at any point during the day or the night, but will forfeit acting the next night if that happens. Sweden cannot die N1 (NK attempt won't appear in the NP).

    Wincon: Outlive two secret countries and the Secret Alliance. Stops game if successful. Must be alive at the beginning of the next phase in order for "outlive" to be counted. Secret targets are drawn at the beginning of the game and are known only to Indy.

    Rules
    * NP shows invasions (kill), protections (saves) and quarantines (trap).
    * DP shows lynched players (no hint if the vote was manipped.
    * Tie: D1 no lynch, D2+ all players in tie are lynched.
    * OOA: Night invasion (kill) >> Blockade (block) > Quarantine (trap) > Protect (save) > Regular invasion > Spy
    * Blockade / Quarantine will be told to the players regardless if they had an action that was blocked or not
    * Regular invasion can be blocked, the SA night invasion cannot be blocked, only saved from
    * Sweden's ODTG RID veto cannot be blocked or saved from as it happens instantly

    Players:

    1. Thalia
    2. bonanova
    3. Molly Mae
    4. Flamebirde
    5. maurice
    6. MikeD
    7. plasmid

    Backups:

    8.
    9.

    Roles are out, Night 1 ends Monday Feb 20th at 9 PM UTC (About UTC). That means 4 PM EST and 11 PM for me.

    • Upvote 1
  7. UN Mafia III

    Secret Alliance: Wincon - Last standing
    China -- The size of the country allowed it to send a replacement for the representative lost in the previous game. Each night chooses a player to target and remove from the game. Action is unstoppable except via save. Will use its electronic interception technologies to find out the identity of the target if target is saved. Once during the game (ODTG) can remove a vote.

    UN Alliance: Wincon - Last standing.
    USA -- The size of the nation and its offensive capabilities, demand it acts but not two nights in a row. Chooses to invade (kill) on even or odd nights at the beginning of the game. Must invade on said night, if no target is drawn it is randomly selected (cannot invade self).

    Germany -- Its economic influence grows steadily which leads to an increase in political influence. Sometimes is forced to save nations in dire need, but would prefer preventing actions. Each night can save a player but there's a 50% chance that this backfires in which case Germany loses its vote the next day.

    Russia -- Has hundreds of satellites floating in space. Can use one per night to spy an alive nation either to see who targeted it or to see who that nation acted upon. Once during the game (ODTG) Russia can instead get lucky and find out a player's true role.

    United Kingdom -- Has worldwide influence among its former colonies. Once per night it can blockade a country, but not the same country twice in a row. Blockading stops any day or night action except for ODTG actions and the Secret Alliance's night invasion.

    Australia -- Has an interesting choice of possibilities due to its cultural diversity. Has 4 agents at its disposal, each can be used once: 1. Add 1 extra secret vote, 2. Remove a vote, 3. Protect (save but cannot be cast on self), 4. Break quarantine (used during the day can make the player quarantined by Sweden able to vote and be voted for).

    Indy
    Sweden -- A nation with nothing to contribute to war and naturally inclined to peace. From time to time, may choose to temporarily side with a Faction or the other, in order to protect its own interests. Each night can quarantine a country but not the same twice in a row. Quarantine acts like a trap - saves from kills / invasions and renders the target neutral - unable to vote the next day or be voted for (but can speak). Once during the game (ODTG) can veto out a country (RID Kill) at any point during the day or the night, but will forfeit acting the next night if that happens. Sweden cannot die N1 (NK attempt won't appear in the NP).

    Wincon: Outlive two secret countries and the Secret Alliance. Stops game if successful. Must be alive at the beginning of the next phase in order for "outlive" to be counted. Secret targets are drawn at the beginning of the game and are known only to Indy.

    Rules
    * NP shows invasions (kill), protections (saves) and quarantines (trap).
    * DP shows lynched players (no hint if the vote was manipped.
    * Tie: D1 no lynch, D2+ all players in tie are lynched.
    * OOA: Night invasion (kill) >> Blockade (block) > Quarantine (trap) > Protect (save) > Regular invasion > Spy
    * Blockade / Quarantine will be told to the players regardless if they had an action that was blocked or not
    * Regular invasion can be blocked, the SA night invasion cannot be blocked, only saved from
    * Sweden's ODTG RID veto cannot be blocked or saved from as it happens instantly

    Players:

    1. Thalia
    2. bonanova
    3. Molly Mae
    4. Flamebirde
    5. maurice
    6. MikeD
    7. plasmid

    Backups:

    8.
    9.

    Okay, finally got around to trimming it up, gonna link this one in my signature as OP and send out the roles in a bit.

  8. 14 hours ago, flamebirde said:

    Well, we have seven (but 6v1v1 is 8, might be able to go 5v2 and dump the indy), so we could do the condensed game. I'll cast my vote for a classic game, just so we can get the show on the road a bit quicker.

     

    I was thinking more like 7 = 1 baddie vs 5 goodies vs 1 indy, hosted 2 Mafias the same size recently so I'm pretty sure I can balance it in a classical setting. If no one signs up till Friday night, I'll trim it, send out the roles and N1 can end Monday.

    The individual wincons can't be balanced for a trimmed version unfortunately. Anyone leaving the game would make it lopsided and I don't see enough ideas of individual wincons to make a miracle in-game balance for events. But I guess I can run it again in the future as a redux of the OP if there are more people interested during the summers for example. So, all is not lost.

    I'd rather have you play since you all showed up and signed up ;)

    • Upvote 1
  9. Well, for me it loads very slowly sometimes, so I shrugged it off as a bandwidth problem.

    But I've seen the daily maintenance message once.

    (Host): araver

    Players: 
    1. Thalia
    2. bonanova
    3. Molly Mae
    4.
    5.
    6.
    7. MikeD
    8.
    9. plasmid
    10.
    11.

    Backups
    1.
    2.

    Voting for:

    * Classic game: Bonanova, plasmid

    * Individual wincons: Molly Mae

    6 more spots open.

    I think I can shrink it down to 7 players (1vs6vs1), but I would need to dump the individual wincons to do so.

  10. 21 hours ago, Molly Mae said:

    I sent Hirk a direct message.  Maybe he'll jump in.

    I told myself I wouldn't mafia again, but eh.  This might be fun.

    EDIT: Is BD super slow for anyone else?  Or just me?  Page loads seem to take forever.  

    It is slower for me as well. Limited bw I guess. But at least it doesn't give 502 error messages.

    Also, since this is filling up but most that signed up don't check daily, I'd like to make it a 48h phase (each day/night lasts 2 days).

  11. 18 hours ago, MikeD said:

    Oh dear! What have i done :)

     

    Questions about the wincons:
     1. Are we informed that a player is trying to leave the game?
     2. If someone leave the game, does the game continue?

    1. No, only the player knows he submitted Leave to the host.

    2. Yes, the game continues up until everyone leaves or there is only one faction left.

    8 hours ago, plasmid said:

    Wow, quoting the roster and removing formatting sure is more difficult on BrainDen.

    I find it next to impossible on phone, but it can be copy-pasted with formatting and colors on a PC :D

  12. (Host): araver

    Players: 
    1. Thalia
    2. bonanova
    3.
    4.
    5.
    6.
    7. MikeD
    8.
    9.
    10.
    11.

    Backups
    1.
    2.

    Voting for:

    * Classic game: Bonanova

    * Individual wincons:  

    Indeed the individual wincons make for a different backstabbing setting possible, but given the long hiatus of games here, I won't push for it now.

    And @MikeD sorry for the lack of spamming. I'll make up for it :D

  13. Oh, and also, you can vote for playing the game with individual wincons OR deleting these wincons and making it a normal Den Game: Goodies versus Baddies versus Indy.

    (I would really appreciate your input on this since in previous games not all players who pushed their team to a winning position actually got to win)

  14. Disclaimer: Although loosely inspired by actual historical events, this story is fictional and not intended to depict any actual person or event.

    UN Mafia III

    Secret Alliance - Have BTSC and a night invasion (kill). NK must be carried out by a player.

    China -- The size of the country allowed it to send a replacement for the representative lost in the previous game. Can use electronic interception technologies. If China can successfully guess the Nation (player) who is the recipient of a message from South Korea, China may read the message (silent intercept) OR replace it with a message of his own (active intercept), but not both. During the day, may secretly change one vote. WINCON: Secretly wants revenge for losing face in recent games. Cannot leave unless both USA and Russia are out of the game.

    North Korea -- Nuclear devices were just a cover for North Korea's top secret project: building a better Google Earth. They have satellites that cover the whole globe. Can spy 1 player per night, even if that player is dead. If they spy Russia, Russia learns their identity as well. WINCON: Doesn't like their Southern neighbors and will do anything to see them eliminated. Cannot leave the game until South Korea is eliminated.

    Iran -- Still walking a thin line, wishes to dominate and prevent other nations of controlling its neighbours. Ability - Each night can hire an external agent. Ability comes after a roll of die - 1. No action  2. RID Kill 3. Spy 4. RID Kill 5. Block 6. No action. WINCON: Can only leave the game if he eliminates a player via personal RID Kill action OR by carrying the NK 2 times.

    UN Alliance - No BTSC, No group abilities.
    USA -- The size of the nation and deployed security makes it impenetrable during some nights. It cannot die at night on odd nights. It's offensive capabilities allow for a RID Kill each even night. WINCON: Must correctly RID Kill 1 baddie or get targeted for a kill (and survive) before attempting to leave the game.

    Russia -- Has hundreds of satellites floating in space. Can use one per night to spy an alive nation. However their spying technology is easy to detect with the right equipment. If an alive member of the Secret Alliance is spied, the Secret Alliance will be notified of the fact that Russia spied one of them (and which of them), but will not be told Russia's identity. WINCON: Must spy one of the three baddies before leaving the game.

    South Korea -- Has a hard time dealing with their pesky northern neighbors. Silently monitors activities and can tell which player targeted which nation (instead of the other way around). S. Korea can also send a message (through the host) to one Nation. The message will be delivered at the beginning of the following day. WINCON: Must successfully deliver two messages to friendly nations. The contents of the messages do not matter, as long as the messages were never intercepted by China. After the second message is delivered successfully, S. Korea may leave the game.

    Germany -- Its economic influence grows steadily which leads to an increase in political influence. Sometimes is forced to save nations in dire need, but would prefer preventing actions. Each night can choose to save a player OR try to guess the Night Kill carrier. If Germany guesses correctly, the NK is blocked (but not the other action of that player). WINCON: Must save (successfully) a player OR guess and block the Night kill to be allowed to leave.

    Australia -- As a penal colony, Australia can imprison one player per night, but not the same player two nights in a row. Target is chosen during the previous day (so there is no action during N1). Imprisoned players cannot act that night and lose BTSC with their teammates if they had any. WINCON: They try to prove that they are just as worthwhile as their allies. Cannot be the first of the UN Alliance to leave the game (they can leave, however, if at least one of the alliance is dead).

    Canada -- Learns the faction of players imprisoned by Australia, but not their role. The size of the country allows vote manipulation (own vote) during the day (x0, x1, or x2). WINCON: Before leaving the game, Canada must lynch one of the Secret Alliance members (final vote is the lynched player and not x0).

    United Kingdom - Has worldwide influence among its former colonies. Starts with no abilities (vanilla), but when one of the English speaking countries (US, Canada, Australia) dies, UK takes over the actions / active abilities of that nation. Every night, UK can choose only one ability to use from the available list. After inheriting abilities, if UK outs that one of the nations has died, it loses all the inherited abilities. WINCON: Cannot leave the game until at least one of USA / Australia / Canada have left the game (or are dead and UK managed to successfully use at least once a inherited ability).

    Indy
    Sweden -- A nation with nothing to contribute to war and naturally inclined to peace. From time to time, may choose to temporarily side with a Faction or the other, in order to protect its own interests. Sweden cannot die N1 (NK attempt won't appear in the NP). Secret WINCON. Secret Ability (1 ability). 

    Rules about WinCons (Goals before leaving the game)
    - All WinCons are to reach an individual goal then leave the game.
    - To leave the game, the player must sacrifice his night ability and declare that he wishes to leave the game (PM host at night). After this declaration, he must survive that night and following day. If he survives both, he may leave.
    - After submitting the LEAVE action, the following day their vote is (secretly) counted x0.
    - Blocks do not prevent a player from leaving, but an imprisonment does. An imprisoned player must be freed before attempting to leave.
    - If a player attempts to leave without completing his assigned goal, he will be informed that he cannot leave only AFTER the night and day cycle have completed.
    - When a single faction manages to eliminate the other faction, there's no one stopping them to leave the game so all alive players from that faction automatically leave/win (this bypasses individual WinCons).

    Other rules:
    - Order of actions is chronological (i.e. all rules are ">>") Imprison >> LEAVE >> Block >> Save / Guess NK >> NK/RID Kill >> Spy >> Message Send/Intercept
    - Night Kill is stopped if target is trapped, imprisoned or saved. NK is also stopped if Germany guesses the NK carrier or the NK carrier is RID Killed or trapped. Night Kill can be redirected.
    - RID Kills can only stopped if target is trapped or arrested (imprisoned) (cannot be stopped by Germany's save or guess)
    - Regular Kill (die-based) can only be stopped if target is trapped, arrested or saved (cannot be stopped by Germany's guess).
    - Redirected spies will not be told they were redirected. Instead, they will receive the role of the person they were redirected to.
    - Night-post will show only successful actions. Spies will not be shown.
    - D1 tie lynch=no lynch. Any other day tie = All tied players are lynched!

    Testing the waters (host): araver

    Players: 
    1.
    2.
    3.
    4.
    5.
    6.
    7.
    8.
    9.
    10.
    11.

    Backups
    1.
    2.

    Since I don't know how many of you have re-accessed your accounts or are able to join or are reading this, or are willing to play ....

    ... I'm just gonna spam everyone who expressed an interest in 2011, 2012, 2013, 2014 (or later) :P and any who played in my games before. And anyone I can think of (and the auto-complete still works)

    @Thalia

    @Yoruichi-san

    @Yodell

    @Molly Mae

    @onetruth

    @Hirkala

    @marksmanjay

    @flamebirde

    @Kikacat123

    @phil1882

    @phaze

    @bonanova

    @BMAD

    @Panther

    @TwoaDay

    @plasmid

    @tolecnal

    @nana77

    @Auramyna

    @dee_tot

    @SuperJack

    @curr3nt

    @maurice_2.0

    @Framm 18

    @plainglazed

    @Logophobic
     

  15. Marking plainglazed's answer as correct since there are no other contestants, even though my answer differs a bit.

    For the record:

    27 ||| 24 = 18 + 2 = 20

    The explanation is that PG's answer is correct up to a point, spoiler below for comments on his solution

    Spoiler

    plainglazed: "Each operand n is converted to the number of positive integers less than n and relatively prime to n.  Then simple addition of the two converted operands yields the result. "

    Araver: True, there is a function f such that a ||| b = f(a) + f(b) = c

    plainglazed: "I said I think this is close because if an n is not prime and converts to a multiple of 4, then it appears that result must be halved before adding to the other half of the operation.  Knowing araver, gotta think there is a more elegant way to describe what appears to be a need for further reduction in certain cases."

    Araver: Indeed

    1) if n is prime f(a)=a-1

    Examples:  f(2) = 1, f(3) = 2, f(5) = 4, f(7) = 6, f(11) = 10, f(13) = 12, f(17) = 16, f(19) = 18, f(23) = 22.

    2) if n is not prime and converts to a multiple of 4 f(a)<=a/2.

    Examples: f(4) = 2, f(8) = 2, f(12) = 2, f(16) = 4, f(20) = 4, f(24) = 2, f(28) = 6, f(32) = 8, f(36) = 8.

    Still don't see a pattern? :D

    Good, because it is not obvious.

    3) if n is not prime the function is more complicated than it seems. Let's see if n = p*q where p and q are distinct primes

    f(6) = 2 where f(2)=1 and f(3)=2

    f(10) = 4 where f(5)=4 and f(2)=1

    f(15) = 4 where f(5)=4 and f(3)=2 

    It looks like a maximum at this point, let's go further

    f(22) = 10 where f(11)=10 and f(2)=1

    f(21) = 6 where f(3)=2 and f(7)=6

    f(33)=10 where f(3)=2 and f(11)=10

    So one could conjecture that f(p*q)=max(f(p),f(q)) where p and q are different primes. *It is actually close but not true.

    This works for 3 numbers as well see: 

    f(30)=4 where f(2)=1, f(3)=2 and f(5)=4

    4) Let's look at f(p*p) where p is a prime

    f(4) = 2 where f(2)=1

    f(9) = 6 where f(3)=2

    f(25)=20 where f(5)=4

    It almost looks like f(p*p)= p*f(p)= p*(p-1)

    The above does not explain what happens in the following cases:

    f(8)=2 where f(2)=1, f(4)=2

    f(16)=4 where f(4)=2, f(8)=2

    f(32)=8 where f(16)=4, f(2)=1 

    f(18)=6 where f(2)=1, f(6)=2 and f(3)=2 and f(9)=6. 

    Confused?

    Yes, PG had the correct idea, that there must be an elegant way to describe the series.

    You can still think about it before clicking the following:

    Spoiler

    The definition of f (or one of the definitions actually) is the Carmichael function.  see https://en.wikipedia.org/wiki/Carmichael_function

    f(n)=b where b is the smallest positive integer such that a^b = 1 (mod n) for every a coprime with n.

    Note that Euler's totient function is similar

    g(n)=c where c is the number of integers up to n that are relatively prime to n.

    However Euler's totient function (which was featured in a previous Mystery Operation btw ;) ) is multiplicative, hence easier to discover.

    Since Euler's theorem states a^g(n)=1 (mod n) it is natural that  f(n) <= g(n)

    First number where they actually differ is 8.

    f(8)=2 while g(8)=4

    It is easy to see that 7^2=1 (mod 8), 5^2 = 1 (mod 8), 3^2=1 (mod 8). So while it is true that a^4=1 (mod 8) for every a coprime with 8, the power of two is sufficient.

    And yes, there is a recursive definition that makes more sense :)

    f(n)= lcm [f(p1^a1), f(p2^a2), ... , f(px^ax)]

    where n =  p1^a1* p2^a2 * ... * px^ax is the unique prime decomposition of n.

    And back to our series, the way to decipher it would have been to guess a composition relation which in this case isn't that simple as it it isn't a multiplicative function. In this case, the hidden formula was:

    f( lcm(a,b) ) = lcm [f(a), f(b)] 

    which gave for f(24) = f( lcm(3,8))= lcm [f(3), f(8)]= lcm (2,2)=2.

     

     

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