Klejnoty:
k - kwadrat
o - kolo
t - trojkat
[tex]3k+o=27 /-o\\3k=27-o /:3\\k=\frac{27-o}3\\\\2k+t+o=24\\2(\frac{27-o}3)+t+o=24\\\frac{54-2o}3+t+\frac{3o}3-24=0\\18-\frac23o+\frac33o-24+t=0\\-6+\frac13o=-t /*(-1)\\6-\frac13o=t\\\\2o+t=21\\2o+6-\frac13o=21\\\frac53o=15 /*\frac35\\o=9\\t=6-3=3\\k=\frac{27-9}3=6\\\\\text{Kolo: 9g, Trojkat: 3g, Kwadrat: 6g}[/tex]
Klodka:
[tex]A, B, C, D \text{ to liczby calkowite z zakresu (0, 9)}\\a=2b\\b+c=13 /-b\\c=13-b\\\\a+b=c+d\\2b+b=13-b+d /+b\\4b=13+d /:4\\b=\frac{13+d}4\\\\\text{Nastepna liczba po 13 ktora dzieli sie na 4 bez reszty, to 16, wiec 16-13=3}\\\\d=3\\b=\frac{13+3}4=\frac{16}4=4\\a=2b=2*4=8\\c=13-b=13-4=9\\\\\text{Kod: } 8493[/tex]
