A mo-Roman sampler

Pluck some relatively easy mo-Roman mini-puzzles while there’s relatively easy pickin’s.

1. What two English words, taken as mo-Roman numerals, form the same number?

Two words other than MILL and MIC, that is, which both form the number 1099 as an example.

MILL   =   M + (−I ) + L + L   =   1000 − 1 + 50 + 50   =   1099
MIC     =   M + (−I ) + C       =   1000 − 1 + 100       =   1099

Mo-Roman numerals use the same digits as Roman numerals but allow infinite variation.   All digits may occur any number of times and in any order. A smaller digit counts negatively each time it occurs anywhere to the left of a larger digit.   Here are two more ways to form 1099.

IDIDCI   =   (−I ) + D + (−I ) + D + C + I          =   −1 + 500 - 1 + 500 + 100 + 1       =  1099
LVMCLIIII   =   (−L) + (−V) + M + C + L + I + I + I + I   =   −50−5+1000+100+50+1+1+1+1   =  1099

Among variations of the number that solves this mini-puzzle are an everyday word and a somewhat technical (not technological) term that also spells a common abbreviation.

2. What is the simplest mo-Roman representation of zero?   (Meant to familiarize, not trick.)

Simplest ?   The fewer the digits the simpler (M is simpler than XX).   For the same number of digits, compare largest digits (LXLI is simpler than VVCI because L is less than C).   Any further ambiguity is decided by persuasive ranting.

3. What is the simplest mo-Roman numeral whose value remains unchanged by removing its last digit?   (Meant to be more interesting than tricky.)

A nonsolution, going from IV to I by removing V, fails because the value changes (from 4 to 1).

4. What is the simplest positive mo-Roman numeral whose value is negated by removing its first digit?

A nonsolution, going from  VI I I I I IV = 4  to  I I I I I IV = −1  by removing V, fails because  −4 ≠ −1.

5. What is the simplest positive mo-Roman numeral whose value is negated by removing its last digit?

A nonsolution, going from  I I I I I IVV = 4  to  I I I I I IV = −1  by removing V, fails because  −4 ≠ −1.

6. What is the simplest positive mo-Roman numeral whose value can be negated by appending a single digit?

A nonsolution, going from  I I I I I I = 6  to  I I I I I IV = −1  by appending V, fails because  −6 ≠ −1.

7. What is the simplest positive mo-Roman numeral whose value can be negated by prepending (adding on the left) a single digit?

A nonsolution, going from  I I I I I IX = 4  to  VI I I I I IX = −1  by prepending V, fails because  −4 ≠ −1.

8. What is the simplest positive mo-Roman numeral whose value is negated by reversing the order of its digits?

A nonsolution, reversing  VI I I I I I = 11  to get  I I I I I IV = −1 , fails because  −11 ≠ −1.

9. What is the simplest mo-Roman representation of zero that
• is asymmetric
• also represents zero when reversed?

A nonsolution, VVVVXX = 0, fails because its reverse, XXVVVV = 40, does not represent 0.

10. What is the simplest mo-Roman representation of zero that
• is asymmetric
• also represents zero when reversed
• includes only one instance of its largest digit?

The same nonsolution, VVVVXX = 0, fails both because its reverse does not represent 0 and because it contains two instances of its largest digit, X.

11. What is the simplest mo-Roman representation of zero that
• is asymmetric
• also represents zero when reversed
• includes only one instance of its largest digit
• begins and ends with different digits?

That nonsolution, VVVVXX = 0, does begin and end with different digits, V and X, but again fails because its reverse does not represent 0 and it contains two instances of its largest digit.

Pick and pluck as you please.   Partial posts are welcome.   The mo-Roman the mo-merrier!

• Is the empty string a solution to #2?
– Deusovi
Apr 28 '17 at 21:19
• Ohohoho, @Deusovi, don't make me edit the puzzle statement to exclude answers that would also work for standard Roman numerals, or that would rewrite mathematical history. (Sorry for the after-edit-period re-comment but:) Now I'm seeing mo-Roman 0s everywhere!
– humn
Apr 28 '17 at 21:33

1 What two English words, taken as mo-Roman numerals, form the same number?

IM(apparently can be used as a noun) and DID = 999
[Intended answer, from Dan Russell: DIM = ID = 499]

2 What is the simplest mo-Roman representation of zero?

I believe the simplest/smallest answer is VVX because V being half of X is the best ratio to nullify the value quickly.

3 What is the simplest mo-Roman numeral whose value remains unchanged by removing its last digit?

VX removing the last X still gives 5.

4 What is the simplest positive mo-Roman numeral whose value is negated by removing its first digit?

XVVVX remove the first X and it goes from 5 to -5

5 What is the simplest positive mo-Roman numeral whose value is negated by removing its last digit?

VVVXX remove the last X and it goes from 5 to -5

6 What is the simplest positive mo-Roman numeral whose value can be negated by appending a single digit?

VVVXVV appending a X will go from 5 to -5

7 What is the simplest positive mo-Roman numeral whose value can be negated by prepending (adding on the left) a single digit?

LLCV goes from 5 to -5 by prepending a X

8 What is the simplest positive mo-Roman numeral whose value is negated by reversing the order of its digits?

XVVVVXV reverting the order will make it go from 5 to -5

9 What is the simplest mo-Roman representation of zero that
• is asymmetric
• also represents zero when reversed?

Yet again, not sure if the best but... VVCLLLLCX

10 What is the simplest mo-Roman representation of zero that
• is asymmetric
• also represents zero when reversed
• includes only one instance of its largest digit?

Seems a bit long, but maybe VIIIIIIIIIIXV is the best...

11 What is the simplest mo-Roman representation of zero that
• is asymmetric
• also represents zero when reversed
• includes only one instance of its largest digit
• begins and ends with different digits?

Assuming 10 is correct, perhaps XVVVVVVVVVVLVV is the best.

• @humn thanks. I will try to fix my 6 now... that was a silly mistake of me. Apr 25 '17 at 7:53
• @humn ah! found the number 3.... so easy... how could I have been so blind >.< Apr 25 '17 at 8:04
• What a recovery on #6 as well, stack reader! If this doesn't get more attention otherwise (and maybe even if it does) you'll get a bounty. (Or maybe that'll be a way to get you to find another #1 . . .) (And thank you for going to the trouble of copying alllll the puzzle statements.)
– humn
Apr 25 '17 at 8:10
• @humn thanks. You can delay the answered check for as long as you want... It would be a shame this original puzzle doesn't get any more attention. I know the feeling. My last puzzle took me 4 hours to make and got like 50 views haha.... Apr 25 '17 at 8:33
• 10 is indeed the optimal solution. You can note that to subtract from that biggest number, you cannot use 1 class smaller number, as it cannot work reversed (say VX becomes XV). And 2 class smaller numbers always have factor of 10 between them. So you always need the shape of V_____X_____V with 10 I anywhere between Vs (as long as it isn't 5 on each side). Apr 25 '17 at 11:13