Let
![ABCDEFGH](/media/m/e/b/b/ebb27e11e714f7cb27bab2990e91ca01.png)
be a parallelepiped with
![AE \parallel BF \parallel CG \parallel DH](/media/m/1/8/8/188185f20e79d3336d6253ba070b4b60.png)
. Prove the inequality
![AF + AH + AC \leq AB + AD + AE + AG.](/media/m/a/8/d/a8dd0131b013de6cc8b038c8b12cd3a2.png)
In what cases does equality hold?
Proposed by France.
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Let $ABCDEFGH$ be a parallelepiped with $AE \parallel BF \parallel CG \parallel DH$. Prove the inequality
$$AF + AH + AC \leq AB + AD + AE + AG.$$
In what cases does equality hold?
Proposed by France.