Let the three resistances are R1,R2 and R3. ∴‌‌‌
R1
R2
=‌
1
2
⇒R1=k,R2=2k In parallel, ‌
1
R
‌=‌
1
R1
+‌
1
R2
+‌
1
R3
‌
1
1
‌=‌
1
k
+‌
1
2k
+‌
1
R3
‌
1
R3
‌=1−‌
1
k
−‌
1
2k
‌=‌
2k−2−1
2k
=‌
2k−3
2k
R3‌=‌
2k
2k−3
If k=1, then R3 is found to be negative, which is impossible. If k=2, then R1=2,R2=4,R3=4 R2=R3, not satisfying the condition of the question that all resistance are unequal. If k=3, then R1=3,R2=6 R3‌=2Ω ∴‌‌‌ Largest resistance ‌‌=6Ω