Consider $33$ two level factors. What is the theoretical minimum number of runs required

to be able to fit a model that includes everything up through $19$ factor interactions.

Answer as an integer.

Question $2(5$ pts$)$

Given the alias structure below, what is the resultion of the design? Answer as a roman

numeral $($use cpaital letters for your roman numeral$).$

A $+$ CDEFH

B $+$ ABCDEFH

C $+$ ADEFH

D $+$ ACEFH

E $+$ ACDFH

F $+$ ACDEH

G $+$ ACDEFGH

H $+$ ACDEF

AB $+$ BCDEFH

AC $+$ DEFH

AD $+$ CEFH

AE $+$ CDFH

AF $+$ CDEH

AG $+$ CDEFGH

AH $+$ CDEF

BC $+$ ABDEFH

BD $+$ ABCEFH

BE $+$ ABCDFH

BF $+$ ABCDEH

BG

BH $+$ ABCDEF

CD $+$ AEFH

CE $+$ ADFH

CF $+$ ADEH

CG $+$ ADEFGH

CH $+$ ADEF

DE $+$ ACFH

DF $+$ ACEH

DG $+$ ACEFGH

DH $+$ ACEF

EF $+$ ACDH

EG $+$ ACDFGH

EH $+$ ACDF

FG $+$ ACDEGH

FH $+$ ACDE

GH $+$ ACDEFG

ABC $+$ BDEFH

ABD $+$ BCEFH

ABE $+$ BCDFH

ABF $+$ BCDEH

ABG $+$ BCDEFGH

ABH $+$ BCDEF

ACD $+$ EFH

ACE $+$ DFH

ACF $+$ DEH

ACG $+$ DEFGH

ACH $+$ DEF

ADE $+$ CFH

ADF $+$ CEH

ADG $+$ CEFGH

ADH $+$ CEF

AEF $+$ CDH

AEG $+$ CDFGH

AEH $+$ CDF

AFG $+$ CDEGH

AFH $+$ CDE

AGH $+$ CDEFG

BCD $+$ ABEFH

BCE $+$ ABDFH

BCF $+$ ABDEH

BCG $+$ ABDEFGH

BCH $+$ ABDEF

BDE $+$ ABCFH

BDF $+$ ABCEH

BDG $+$ ABCEFGH

BDH $+$ ABCEF

BEF $+$ ABCDH

BEG $+$ ABCDFGH

BEH $+$ ABCDF

BFG $+$ ABCDEGH

BFH $+$ ABCDE

BGH $+$ ABCDEFG

CDG $+$ AEFGH

CEG $+$ ADFGH

CFG $+$ ADEGH

CGH $+$ ADEFG

DEG $+$ ACFGH

DFG $+$ ACEGH

DGH $+$ ACEFG

EFG $+$ ACDGH

EGH $+$ ACDFG

FGH $+$ ACDEG

ABCD $+$ BEFH

ABCE $+$ BDFH

ABCF $+$ BDEH

ABCG $+$ BDEFGH

ABCH $+$ BDEF

ABDE $+$ BCFH

ABDF $+$ BCEH

ABDG $+$ BCEFGH

ABDH $+$ BCEF

ABEF $+$ BCDH

ABEG $+$ BCDFGH

ABEH $+$ BCDF

ABFG $+$ BCDEGH

ABFH $+$ BCDE

ABGH $+$ BCDEFG

ACDG $+$ EFGH

ACEG $+$ DFGH

ACFG $+$ DEGH

ACGH $+$ DEFG

ADEG $+$ CFGH

ADFG $+$ CEGH

ADGH $+$ CEFG

AEFG $+$ CDGH

AEGH $+$ CDFG

AFGH $+$ CDEG

BCDG $+$ ABEFGH

BCEG $+$ ABDFGH

BCFG $+$ ABDEGH

BCGH $+$ ABDEFG

BDEG $+$ ABCFGH

BDFG $+$ ABCEGH

BDGH $+$ ABCEFG

BEFG $+$ ABCDGH

BEGH $+$ ABCDFG

BFGH $+$ ABCDEG

ABCDG $+$ BEFGH

ABCEG $+$ BDFGH

ABCFG $+$ BDEGH

ABCGH $+$ BDEFG

ABDEG $+$ BCFGH

ABDFG $+$ BCEGH

ABDGH $+$ BCEFG

ABEFG $+$ BCDGH

ABEGH $+$ BCDFG

ABFGH $+$ BCDEG