Answer
See the answer below.
Work Step by Step
a) The choice must be: heating the one with higher mass and specific heat capacity (1) and cooling the one with lowest mass and specific heat capacity (4).
$100\ g\times 0.9002\ J/g.K \times(T-100)+$
$50\ g \times 0.1289\ J/g.K \times (T--10)+$
$300\ g\times4.184\ J/g.K\times (T-21)=0$;
$90.02(T-100)+6.45(T+10)+$
$1255.20(T-21)=0$;
$35297=1352T$;
$T=26.1^{\circ}C$
b) For this to happen, the energies provided and removed by the metal pieces must cancel each other:
$C_1(100-21)=C_2(21--10)$
$C_1/C_2=0.392$
Which is closest to heating 6 and cooling 2:
$0.3860\times 50\div0.9002\div50=0.429$
$50\ g\times 0.3860\ J/g.K \times(T-100)+$
$50\ g \times 0.9002\ J/g.K \times (T--10)+$
$300\ g\times4.184\ J/g.K\times (T-21)=0$;
$19.3(T-100)+45.1(T+10)+$
$1255.20(T-21)=0$;
$27838.2=1319.5T$;
$T=21.10^{\circ}C$
