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19 = XIX

49 = XLIX

99 = XCIX

Expected result is 167 = CLXVII

Method 1: Convert subtractive pairs so IV becomes IIII, XL becomes XXXX and XC becomes LXXXX. Then sort values in descending order of value, grouping C, X and I in groups of 5, and L and V in groups of 2, then reduce these groups so that IIIII becomes V, VV becomes X, XXXXX becomes L and LL becomes C.

XIX + XLIX + XCIX =

XVIIII + XXXXVIIII + LXXXXVIIII =

L + XXXXX + XXXX + VV + V + IIIII + IIIII + II =

L + XXXXX + XXXX + VV + VV + V + II =

L + XXXXX + XXXXX + X + V + II =

LL + L + X + V + II =

C + L + X + V + II =

CLXVII

Method 2: Expand all symbols into positive and negative symbols, sort by absolute value, cancel out any similar values with opposing signs. Convert higher values to lower values as required.

XIX + XLIX + XCIX =

X - I + X - X + L - I + X - X + C - I + X =

C + L + X + X - X + X - X + X - I - I - I =

C + L + X + X - I - I - I =

C + L + X + V + V - I - I - I =

C + L + X + V + I + I + I + I + I - I - I - I =

C + L + X + V + I + I =

CLXVII

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