rqtr

Begubtencuvp cebwrpgvba nybat gur yvar pbaarpgvat nal rqtr zvqcbvag gb gur bccbfvgr rqtr zvqcbvag tvirf n fdhner, lvryqvat 3 fhpu cebwrpgvbaf (cyhf gurve bccbfvgr pbhagrecnegf).

Va gur bgure pnfr, (3), guerr bs gur cbvagf ner ba gur erpgnatyr uhyy (cbffvoyl jvgu n cnve ba gur fnzr rqtr).

My attempt was similar, but I didn't zragvba gur rqtr pnfrf so I may not have received full credit from the grader (they don't tell you which question your points come from).

(Jr trg guerr fbyhgvba cbyltbaf sbe rnpu bs gubfr, bar sbe rnpu cbvag vafvqr gur erpgnatyr ohg bhgfvqr gur gevnatyr, naq abar sbe gur barf juvpu yvr ba na rqtr).

Gur pbhag bs cbyltbaf sebz guvf vf fvzcyl gur pbhag bs havdhr frgf bs 4-cbvagf ylvat ba fhpu erpgnatyrf (pbzovangbevny sbezhyn: ovt grez vf N^2 O^2 (bar ba rnpu rqtr -- # vf whfg gur cebqhpg bs rqtr yratguf), cyhf gur pnfrf jurer cnvef bs cbvagf ner ba gur fnzr rqtr (funer k- be l-) (cbffvoyl gjb cnvef -- guvax (2,0) (1,0) (0,1) (0,2)), zvahf gur pnfrf jurer gurl uvg gur fnzr pbeare).

Rahzrengvat gur pnfrf; nal sbhe cbvagf qrsvar n erpnagthyne "uhyy": [(zva n_k, znk_k)] K [zva n_l, znk n_l)] ('n' enatvat bire gur sbhe cbvagf) Va gur pnfrf bs vagrerfg (3) be (4), ng yrnfg guerr bs gur cbvagf yvr ba gur rkgrevbe rqtr bs guvf uhyy.

Rahzrengvat gur pnfrf; nal sbhe cbvagf qrsvar n erpnagthyne "uhyy": [(zva n_k, znk_k)] K [zva n_l, znk n_l)] ('n' enatvat bire gur sbhe cbvagf) Va gur pnfrf bs vagrerfg (3) be (4), ng yrnfg guerr bs gur cbvagf yvr ba gur rkgrevbe rqtr bs guvf uhyy.