unreality

~~~ Round Ten ~~~ Panther Freeze - Dawh Shield - dms172 Curse - FIF Coup de Grace - FIF RODB Dawh Freeze: Panther Shield: FIF Curse: CL Coup de Grace: Frost Flummox: Frost Vacuum: Dawh Spell of Choice: Vacuum Warp (70% spells cast on me) DMS * Freeze - Dawh * Shield - Frost * Curse - FIF * Coup de Grace - FIF * Flummox -Dawh * Vacuum - Dawh * RODB Round Ten coming earlier than usual, but I have the time and everyone PMed This just means you guys get 25 hours until Round Eleven PMs * Surprisingly, Dawh's Vacuum succeeded! And he Vacuumed himself! And he cast Vacuum Warp on himself! Lol it may sound rigged but his Vacuum actually did succeed, I didn't even see the other stuff until afterwards. This will be interesting. I rolled the d100 but unfortunately got a 76, which is part of the section where he Vacuums up spells cast BY him. His Vacuum Warp came very close to uber-defending himself, unfortunately it didn't work. So the rest of the spells cast by Dawh fail * Flummoxes don't matter because Panther didn't Flummox anybody and DMS Flummoxed Dawh, who can't cast any spells anyway * Panther and DMS both cast Freeze on Dawh, however because it was only two people, there was only a 1/3 chance of paralyzing Dawh next turn, and it failed. So NOBODY is paralyzed for Round Eleven * After Shields and Curses: Duel Master: Unreality 1) Frost - 6 2) Frozen in Fire - 0 3) CL - 6 4) Panther - 7 5) Dawh - 4 6) DMS - 8 * Rain of Dual Bombardment has no effect in THIS round because no Hexquakes were cast, however, both Panther and DMS cast RoDB, thus Round Eleven is a Double Round!!! Coming back to that in a second * Both Panther and DMS Coup de Graced FIF. Sorry Frozen! Duel Master: Unreality 1) Frost - 6 2) Frozen in Fire - DEAD 3) CL - 6 4) Panther - 7 5) Dawh - 4 6) DMS - 8 There are only five players left for Round Eleven! And better yet, Round Eleven is a double round! In the Double Round, all Curses take away 2 Shield Points instead of one, and Coup de Grace has a 50% chance of success on people with 1 SP in addition to the usual 100% chance of success on people with 0 SP. In the Round-Five-Double-Round, it had an effect on Freeze as well, but because the rules for Freeze have changed, I'm adding a different effect to the Round-Eleven-Double-Round: everyone can cast TWO Spells of Choice! This is the current SoC list: * Spell of Choice - for this spell, you choose from your diverse arsenal of magic: [None of these spells have specific targets, they affect the group as a whole] ** Hexquake - everyone either loses 1 Shield Point (70%) or gains 1 (30%), including yourself ** Magelore - unlocks a new Spell of Choice for everyone to use ** Aqua Vida - gives 2 Shield Points to the mage with the least amount of SP, if there are multiple mages of that amount then the target is chosen randomly from those people ** Magnetic Surge - all Flummoxes move up by 4%. Ie, originally they have a 25% chance. For each Magnetic Surge cast in the round, however, the chance increases by 4%. This value is totaled before the Flummoxes are rolled ** Quid Pro Quo I - everyone that cast Shield on you during the round gains 1 Shield Point themselves ** Quid Pro Quo II - everyone that cast Curse on you during the round loses 1 Shield Point themselves ** Ascension - [takes effect before anything else] during the round that you used it in, your rank is as if it subtracted 5. For example, the 5th person becomes 5-5 = rank 0. The 3rd person becomes 3-5 = -2. This gives the upper hand in Vacuums and Flummoxes ** Assassin Bolt - your Coup de Grace spell is amplified to affect not just the person you selected but the person above and below them, ignoring Vacuums on either of the three targets or on you. This takes affect no matter what, even if you are one of the adjacent victims (remember that Coup de Grace only succeeds if someone's SP is 0, and Assassin Bolt just triples the Coup de Graces you get and makes them unstoppable) ** Vacuum Warp - [takes effect after Ascension, before Vacuums] this spell will affect the Vacuum-type chance. Normally it's 1/2 and 1/2 whether the Vacuum will absorb all spells cast ON the person or all spells cast BY the person. When you cast Vacuum Warp, you change the chances to 70% & 30%, weighted in either direction, which you choose (for example, "Vacuum Warp - 70% spells cast on me, 30% spells cast by me") ** Aqua Excessum - this spell poisons the reviving water of the Aqua Vida spell, causing it to take away 2 Shield Points from the lowest instead of giving 2 SPs. Aqua Excessum obviously has no effect if Aqua Vida is not cast in the same round ** Rain of Dual Bombardment - harness of the power of weather to bring a ripple of devastating energy into the Duel Chamber! Not only does the Rain of Dual Bombardment bring about a Double Round the next round IF and only if EXACTLY TWO Dual Bombardment spells are cast, regardless of that, the Rain morphs the power of the other natural disaster spell: Hexquakes. The Rain allows you to transfer up to 5% of one the chances to the other, and multiple people using Rain all combine their effects on Hexquake. The Rain of Dual Bombardment may cause other random, adverse changes on the Hexquake spell as well ** Spellguard - also known as the Antiflummox, this spell forges a barrier of force that surrounds and protects your spells from confusion and switching. In the round that you cast Spellguard, all Flummoxes used against you fail. Spellguard takes effect AFTER Vacuums Good luck in Round Eleven! The roster: (nobody is paralyzed) Duel Master: Unreality 1) Frost - 6 2) CL - 6 3) Panther - 7 4) Dawh - 4 5) DMS - 8

Yeah I figure NODE will be useful (though you would need an EDIT line between NODE and JUMP to control the a-value of the NODE), however it may not actually be as useful as you may think. Even if a BOMB gets planted in one of the lines, the executor will run that just the same if it's told to with NODE. Now that I think about it, the only benefit of NODE that I can see right now is if you want to continually jump 2 forward, skipping a line, and don't want to waste JUMPs to accelerate you to the next spot or something, you could use a NODE-EDIT-JUMP combo to execute only certain lines that you want to. You could put a com() or similar function in the EDIT's b-value that takes input and decides which line to execute next with NODE.... so basically NODE can be used to execute lines in any which order, as long as you have a logical pattern of what the next node to execute is. But it would be more efficient to put them in the best of order as possible with the occasional JUMP or whatever rather than use NODE, because a NODE-EDIT-JUMP combo only executes one line every third Oh wait a minute, you don't need the EDIT between NODE and JUMP! I see what you mean, you can just use a com() for the NODE's a-value and evaluate input... no EDIT needed. So it's a NODE-JUMP combo. A bit more efficient, but still, NODEs should only be used when it's the best option, though an occasional NODE might be good. It all depends on the program as for SPLIT and MERGE, yeah I was going for more control over the executors too, however as taliesin pointed out, it can get too complicated and paradoxical So I propose a new command: FLIP. It reverses the order of your executors, making the older one count as the most recently made, etc. So if you had four executors like this: 1: initial executor 2: second executor 3: third 4: fourth 5: N/A and any one of those executors hit a FLIP command, the new order would be this: 1: fourth 2: third 3: second executor 4: initial executor 5: N/A and so if it was the SECOND EXECUTOR that hit the FLIP command, the next executor to run wouldn't be the third, it would be the FIRST EXECUTOR. I think this could add some control in deciding which executor to MERGE. What do you guys think? fool: How much simpler do you think you could make Swarm now, with these new ones? Just curious Also, does anyone have any more ideas?

This should be in Jokes

I said yes... and for someone that likes knowledge, that may seem contradictory, but it's kind of hard to explain I like learning new things, but sometimes the new things themselves aren't the greatest Though if I had any choice, I would rather be Knowing and only Somewhat Blissful rather than Unknowing and Completely Blissful, so maybe I should've picked No... hmmm...

* the functions don't need grouping, no need to make it more complicated, they're fine as they are * commands should all be 4 or 5 letters long. I was originally hoping to make them all exactly 4, but it wasn't to be so The functions stay, and EDITI stays * I could change NODE to RUN [and in my emulator add an extra space or letter to make it 4 letters], but I like NODE better I suppose RUN does fit the purpose of the command better though... hmm... I'll think on this one * you can't use strings like a or b or c, because the sole point of having an EDITX command (instead of a constant EDIT command) is that you're planning on changing the a/b/c part about it, which means you have to be able to edit the c value of EDITX and change it to something. Because of this, it needs to be a number for both retrieving of it with the c(n) function as well as changing it with the EDITC or EDITX command. Thus a/b/c are represented by numbers. Though I could've picked anything, I think 0/1/2 was the best choice, and can be handled the best mathetically with the mod(m,n) function and whatnot for more efficiency... though if you think they should be represented by different numbers, say so ;D any ideas for new commands? I thought about a few possible ones, then decided against all of them

1. Always avoid alliteration. 2. Prepositions are not words to end sentences with. 3. Avoid cliches like the plague—they're old hat. 4. Employ the vernacular. 5. Eschew ampersands & abbreviations, etc. 6. Parenthetical remarks (however relevant) are unnecessary. 7. Parenthetical words however must be enclosed in commas. 8. It is wrong to ever split an infinitive. 9. Contractions aren't necessary. 10. Do not use a foreign word when there is an adequate English quid pro quo. 11. One should never generalize. 12. Eliminate quotations. As Ralph Waldo Emerson once said: "I hate quotations. Tell me what you know." 13. Comparisons are as bad as cliches. 14. Don't be redundant; don't use more words than necessary; it's highly superfluous. 15. It behooves you to avoid archaic expressions. 16. Avoid archaeic spellings too. 17. Understatement is always best. 18. Exaggeration is a billion times worse than understatement. 19. One-word sentences? Eliminate. Always! 20. Analogies in writing are like feathers on a snake. 21. The passive voice should not be used. 22. Go around the barn at high noon to avoid colloquialisms. 23. Don't repeat yourself, or say again what you have said before. 24. Who needs rhetorical questions? 25. Don't use commas, that, are not, necessary. 26. Do not use hyperbole; not one in a million can do it effectively. 27. Never use a big word when a diminutive alternative would suffice. 28. Subject and verb always has to agree. 29. Be more or less specific. 30. Placing a comma between subject and predicate, is not correct. 31. Use youre spell chekker to avoid mispeling and to catch typograhpical errers. 32. Don't repeat yourself, or say again what you have said before. 33. Don't be redundant. 34. Use the apostrophe in it's proper place and omit it when its not needed. 35. Don't never use no double negatives. 36. Poofread carefully to see if you any words out. 37. Hopefully, you will use words correctly, irregardless of how others use them. 38. Eschew obfuscation. 39. No sentence fragments. 40. Don't indulge in sesquipedalian lexicological constructions. 41. A writer must not shift your point of view. 42. Don't overuse exclamation marks!! 43. Place pronouns as close as possible, especially in long sentences, as of 10 or more words, to their antecedents. 44. Writing carefully, dangling participles must be avoided. 45. If any word is improper at the end of a sentence, a linking verb is. 46. Avoid trendy locutions that sound flaky. 47. Everyone should be careful to use a singular pronoun with singular nouns in their writing. 48. Always pick on the correct idiom. 49. The adverb always follows the verb. 50. Take the bull by the hand and avoid mixing metaphors. 51. If you reread your work, you can find on rereading a great deal of repetition can be by rereading and editing. 52. And always be sure to finish what

I'm an atheist but I still see good ol' Jesus ;D

np Have fun out there in the big Den ;D

* I see what you mean about the indexes. I'll remove that stuff * there's no reason to put "if" in front of each one, that's implied * I thought about adding rand(m,n) ... I guess it could be useful in placing random bombs or something, though people that use it should be cautious of course ;D I'll add it * No, no num(). Like I've said a hundred times, if we have a different variety, such as 3 programs in a 300-node VNA, everyone will be informed long beforehand and can edit their programs. Having constants for each pre-known setting just clutters code. No num() or ANY other function constants, and this is the last time I'm saying this lol anyway, thanks for the help and the suggestions! This is the newest: VNA 2.0 The commands: COPY a,b copies line a into line b (overriding the current line b) JUMP a jumps execution to line a BOMB destroys the executor that executed this node SPLIT a creates a new executor which begins running at line a. Cannot create more than five MERGE deletes the most recently created executor. Cannot delete the initial executor EDITA a,b a is the line number, b is the new a value for that node EDITB a,b a is the line nummber, b is the new b value for that node EDITC a,b a is the line number, b is the new c value for that node EDITX a,b,c a is the line number, b is the new value, c is 0/1/2 to denote a/b/c to change BLANK what the original VNA is filled with. You can use BLANK commands too, it's basically a "do-nothing" command. BLANKs cannot hold a/b/c values like other commands can NODE a execute the command denoted by line a as if it was the current line EDITI a,b,c a = line number, b is how much is added to the current value, and c is 0/1/2 to denote a/b/c to change. 'I' stands for increment The functions: a(n) returns the a value of the node at line n b(n) returns the b value of the node at line n c(n) returns the c value of the node at line n add(m,n) returns m+n sub(m,n) returns m-n mul(m,n) returns m*n div(m,n) returns m/n mod(m,n) returns the remainder of m/n pow(m,n) returns m^n log(m,n) returns log base m of n base(m,n,o) returns m converted from base n to base o. Both n and o must be less than or equal to 10 abs(n) returns the absolute value of n int(n) returns the integer part of n com(m,n,o,p,q) compares m & n. If they are equal, returns o. If m>n, returns p. If n>m, returns q equ(m,n,o,p) compares m & n. If they are equal, returns o. Otherwise, returns p geq(m,n,o,p) compares m & n. If m>n or m=n, return o. Otherwise, p leq(m,n,o,p) compares m & n. If m<n or m=n, return o. Otherwise, p exe() returns the number of executors that you have currently running rand(m,n) returns a random integer from m to n, inclusive. n>m [/codebox]

Not exactly elegant, but I don't think there are any smaller solutions. Can anyone find a non-brute force way to find that solution? Let me retry, scratching my old post on this topic. I'll make a new equation.

Coflux only applies if they initially select to Curse someone without Shielding, or vice versa. All throughout the game, due to Flummoxes (like in this case) or Vacuums or some other effect, people have had Shields take effect without Curses, and vice versa DMS: yes Dawh answered your question Your Shield on Frost got switched with your Freeze on nobody

It was actually 3.17623. The totaled efficiency for x from 1 to 10,000 was 31762.3, then it divides by 10,000. As for why, I have no idea. 100 iterations is about 3.0something, and 1000 was 3.14 I think (that got me pi-excited, but alas it was not to be so ;D) and 10,000 was 3.17623 and took forever on my graphing calculator [yes I made it with my graphing calculator lol]. Because of this slow convergence, and because there really is no definition of 'slow' when you're looking at infinity (), I'm thinking you may be right about it being log base 2 of 10. After dinner, I'll think more on it and possibly make a new program on my computer and calculate to more iterations

Excellent!!! Great puzzle Ysan, and great work guys Yes I'm only here cuz of the link in Ysan's sig ;D

Ah that makes sense... why didn't he tell me? I could've done something about it. That actually works out based on what happens in Round Nine, you'll see ;D ~~~ Round Nine ~~~ Frost Freeze - Frozen Shield - DMS Curse - Frozen Coup de Grace - Frozen Flummox - Dawh Vacuum - Dawh Aqua Vida Frozen [No PM] Dawh Freeze: CL Shield: FIF Curse: CL Coup de Grace: PG Flummox: DMS Vacuum: Frost Spell of Choice: QPQ II DMS * Freeze - [Nobody] * Shield - Frost * Curse - FIF * Coup de Grace - PG * Flummox -Dawh * Vacuum - Dawh * Aqua Excessum With 3/7 paralyzed and one not PMing, Round Nine only consists of three people's spells! ;D * No Vacuums succeed (not surprisingly ) * Only Dawh's Flummox worked, and he Flummoxes DMS's Freeze and Shield * For Freezes, Frozen and Cherry Lane are paralyzed next round, though DMS was Flummoxed by Dawh and thus Freezes Frost while Shielding nobody. So Frost, Frozen and CL are paralyzed for next round * Shields and Curses: Duel Master: Unreality 1) Frost - 5 2) Frozen in Fire - 1 3) CL - 6 4) PG - 1 5) Panther - 7 6) Dawh - 4 7) DMS - 7 Nobody cursed Dawh, so his QPQ II has no effect Next, the deadly combination of Aqua Vida and Aqua Excessum causes the person with the least amount of Shield Points to lose 2! Those in question are either FIF or PG. I'll roll an 8-sided die to determine which one is affected, odd for PG and even for FIF. I rolled a 1, so PG is subtracted 2, thus she's at the lower limit, which is 0: Duel Master: Unreality 1) Frost - 5 2) Frozen in Fire - 1 3) CL - 6 4) PG - 0 5) Panther - 7 6) Dawh - 4 7) DMS - 7 Dawh and DMS Coup de Graced PG, so she is dead and out of the game Duel Master: Unreality 1) Frost - 5 2) Frozen in Fire - 1 3) CL - 6 4) PG - DEAD 5) Panther - 7 6) Dawh - 4 7) DMS - 7 CL, Frost and Frozen are paralyzed for next round, so adding the double asterisks for them: Duel Master: Unreality 1) Frost - 5 ** 2) Frozen in Fire - 1 ** 3) CL - 6 ** 4) Panther - 7 5) Dawh - 4 6) DMS - 7 Wow! We've reached the point where half of the players are paralyzed, and this point I decided from the very beginning to be the turning point for the spell 'Freeze'. From now on, Freeze only takes effect if exactly three players use it on the same person, and if only two use it on the same person, it has a 1/3 chance of success. Sorry Puzzlegirl! Despite your low health, you narrowly escaped death a few times and perservered pretty far Next round is Round Ten! Panther, Dawh and DMS should have their PMs in to me in roughly 20 hours ;D Though if some are late, I will wait up until 24 hours from now

I'm about 2-3 hours over Oops... I guess I was waiting for Frozen, but he still hasn't PMed, so just three people are casting spells today Round Nine summary coming soon ;D

Hmm, well mine already uses indexes, 1-5 to store which executor is at which line and which one is running next. I designed the SPLIT and MERGE functions so that you don't have to change anything and it works exactly the same as it did before, ie, SPLIT a,0 is the same as SPLIT a before, and MERGE 0 is the same as MERGE before. So you don't even need to change your code. Though for those that want more control over their executors, SPLIT and MERGE have more versatility now num() = no. Cuz then we'd have to add other functions returning other constant values such as 30 and 170. num() will always be 200, so we don't need it pi, phi, e = good idea. I'll remove those. Especially cuz I'm not using the other constant (num) float = this could be necessary. If we add int(n) we might as well add float(n). Although: float(n) = sub(n,int(n)) so you're right... it's unncessary to add float(n). I'll remove it too VNA 2.0 The commands: COPY a,b copies line a into line b (overriding the current line b) JUMP a jumps execution to line a BOMB destroys the executor that executed this node SPLIT a,b creates a new executor which begins running at line a. b is the index of the executor, from 1 to 5. Use to 0 for b to denote add(exe(),1), in other words fill the next available spot MERGE a deletes the executor signified by a (1-5). Use 0 to denote the executor with the highest index EDITA a,b a is the line number, b is the new a value for that node EDITB a,b a is the line nummber, b is the new b value for that node EDITC a,b a is the line number, b is the new c value for that node EDITX a,b,c a is the line number, b is the new value, c is 0/1/2 to denote a/b/c to change BLANK what the original VNA is filled with. You can use BLANK commands too, it's basically a "do-nothing" command. BLANKs cannot hold a/b/c values like other commands can NODE a execute the command denoted by line a as if it was the current line EDITI a,b,c a = line number, b is how much is added to the current value, and c is 0/1/2 to denote a/b/c to change. 'I' stands for increment SWAP a the current executor trades index numbers with executor 'a' So, a/b/c values are either numbers (usually line numbers, remember that each node refers to itself as line 0) OR functions. So what are functions? The functions: a(n) returns the a value of the node at line n b(n) returns the b value of the node at line n c(n) returns the c value of the node at line n add(m,n) returns m+n sub(m,n) returns m-n mul(m,n) returns m*n div(m,n) returns m/n mod(m,n) returns the remainder of m/n pow(m,n) returns m^n log(m,n) returns log base m of n base(m,n,o) returns m converted from base n to base o. Both n and o must be less than or equal to 10 abs(n) returns the absolute value of n int(n) returns the integer part of n com(m,n,o,p,q) compares m & n. If they are equal, returns o. If m>n, returns p. If n>m, returns q equ(m,n,o,p) compares m & n. If they are equal, returns o. Otherwise, returns p geq(m,n,o,p) compares m & n. If m>n or m=n, return o. Otherwise, p leq(m,n,o,p) compares m & n. If m<n or m=n, return o. Otherwise, p exe() returns the number of executors that you have currently running high() returns the highest executor index line(n) returns the line # that executor n is running at. n must be from 1 to 5. Use 0 to denote the executor with the highest index [/codebox]

Yeah, the qubit can be 0, 1 or the superposition of 0 AND 1 ;D Not sure what the difference there is between that and tertiary though, since isn't 0/1 kind of like 2, or can you separate 0/1 into ones and zeroes or something? Ross: This is as far as I know, cuz I made a program that uses my one-time equation in post 5 to calculate averages I calculated 10|2 out to the 10,000th iteration and the average was around 3.17 or something like that (earlier it was 3.14 and I thought it might be pi, I got excited, but no ), so unless it converges veeeery slowly, it's not going to be 3.22ish that log base 2 of 10 is. Hmmm... I will think more about this though

VNA 2.0 The commands: COPY a,b copies line a into line b (overriding the current line b) JUMP a jumps execution to line a BOMB destroys the executor that executed this node SPLIT a,b creates a new executor which begins running at line a. b is the index of the executor, from 1 to 5. Use to 0 for b to denote add(exe(),1), in other words fill the next available spot MERGE a deletes the executor signified by a (1-5). Use 0 to denote the executor with the highest index EDITA a,b a is the line number, b is the new a value for that node EDITB a,b a is the line nummber, b is the new b value for that node EDITC a,b a is the line number, b is the new c value for that node EDITX a,b,c a is the line number, b is the new value, c is 0/1/2 to denote a/b/c to change BLANK what the original VNA is filled with. You can use BLANK commands too, it's basically a "do-nothing" command. BLANKs cannot hold a/b/c values like other commands can NODE a execute the command denoted by line a as if it was the current line EDITI a,b,c a = line number, b is how much is added to the current value, and c is 0/1/2 to denote a/b/c to change. 'I' stands for increment SWAP a the current executor trades index numbers with executor 'a' So, a/b/c values are either numbers (usually line numbers, remember that each node refers to itself as line 0) OR functions. So what are functions? The functions: a(n) returns the a value of the node at line n b(n) returns the b value of the node at line n c(n) returns the c value of the node at line n add(m,n) returns m+n sub(m,n) returns m-n mul(m,n) returns m*n div(m,n) returns m/n mod(m,n) returns the remainder of m/n pow(m,n) returns m^n log(m,n) returns log base m of n base(m,n,o) returns m converted from base n to base o. Both n and o must be less than or equal to 10 abs(n) returns the absolute value of n int(n) returns the integer part of n float(n) returns the float part of n com(m,n,o,p,q) compares m & n. If they are equal, returns o. If m>n, returns p. If n>m, returns q equ(m,n,o,p) compares m & n. If they are equal, returns o. Otherwise, returns p geq(m,n,o,p) compares m & n. If m>n or m=n, return o. Otherwise, p leq(m,n,o,p) compares m & n. If m<n or m=n, return o. Otherwise, p exe() returns the number of executors that you have currently running high() returns the highest executor index line(n) returns the line # that executor n is running at. n must be from 1 to 5. Use 0 to denote the executor with the highest index e() returns the constant, e pi() returns the constant, pi phi() returns the constant, the golden ratio [/codebox] What do you think? If we like it, I can change my emulator I was going to add trigonometric functions, then decided against it, though I still left the pi constant. As you can see, for commands I changed SPLIT and MERGE, then added EDITX, NODE, EDITI and SWAP. For functions, I added log, base, int, float, equ, geq, leq, high, line, e, pi and phi. I also took away num because it's always 200 lines with max size 30 and program range 30 to 170 away. If that changes we'll know beforehand So yeah, this should add more functionality and ease for making even better programs ;D I'm sure some crazy stuff can be done with NODE and EDITX (EDITI is just a convenience because I noticed that most EDITs are used to add something to the pre-existing value) and the other stuff I added

Yeah... base-2 is one of the most practical, if not the most, at least with the technology we have today. This problem is focused entirely on the storage efficiency of digits in one base over another, regardless of whether you're using a computer or scratching symbols in the dirt. Actually this problem is specifically geared to the overall average digit-storage efficiency of base 10 over base 2

Yes, I used to think that base-2 was only used because that's what's been used since the origin of computers, however base 2 is actually the most cost efficient for storing numbers unless they can make base 10 storage cost about 3 times more or LESS than 3 times more. Which is why this problem has a lot of practical application edit: You saw my equation in post #5, right?

Yes, the original riddle was going to be something like this: "It costs 4.5 times more money [just a BSed number] for a computer chip to work in base 10 than in base 2... since it can hold 5 times the space, there's a gain in money" but of course that's wrong, because the MAXIMUM efficiency for 10|2 is 4 (at 8 & 9). But then I just decided to make the riddle purely mathematical.

Why do you need to feed all the data?

Do you mean: IX + VI ≠ X You could take any of the I's, really. IX + VI ≠ X X + VI ≠ XI IX + V ≠ XI IX - VI ≠ XI