My teammates showed me this problem. North opened a normal 1♥ opening playing 5 card majors. East came in with 3♦ and South now has a problem. He likes his hand, but has horrible shape. He bids 3♥ which can include a wide range of hands (such as those without much value, but with trump length). He felt that he might have taken the push, but was unhappy about it.
North has some nice features to his hand. The singleton diamond opposite support is good, but he is near minimum in terms of strength. Should he take the push?
3♦ didn't leave much room. Only pass, double, and 3♥ are available below game. Is it just bad luck that they missed it or should one of them taken the push?

Help

1♥ - (3♦) - 3♥ - All Pass