Gold cube distribution

The king cannot decide how to distribute 4 cubes of pure gold, which have edges of length 3 cm, 4 cm, 5 cm, and 6 cm, to two sons as fairly as possible.
Design a solution so that the cubes do not have to be cut.

Final Answer:

x = 1+2+3:4

Step-by-step explanation:

$$\begin{gathered} a=3\text{cm} \\ b=4\text{cm} \\ c=5\text{cm} \\ d=6\text{cm} \\ {V}_1=a^3=3^3=27{\text{cm}}^3 \\ {V}_2=b^3=4^3=64{\text{cm}}^3 \\ {V}_3=c^3=5^3=125{\text{cm}}^3 \\ {V}_4=d^3=6^3=216{\text{cm}}^3 \\ s=(V_1+V_2+V_3+V_4)/2=(27+64+125+216)/2=216{\text{cm}}^3 \\ {s}_1=V_1+V_2+V_3=27+64+125=216{\text{cm}}^3 \\ {s}_2=V_4=216{\text{cm}}^3 \\ x=1+2+3:4 \end{gathered}$$

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