An Infinite Orchard

The final paragraph on the topic alludes to Olber&#x27;s paradox, but stars are not infinitesimally small, so I do not think the argument applies here (though the Big Bang makes the question moot anyway.)<p><a href="http:&#x2F;&#x2F;cmb.physics.wisc.edu&#x2F;pub&#x2F;tutorial&#x2F;olbers.html" rel="nofollow">http:&#x2F;&#x2F;cmb.physics.wisc.edu&#x2F;pub&#x2F;tutorial&#x2F;olbers.html</a>

In the final problem, as the apple trees can be in more than one line, the minimal valid solution is 9 trees, not 12.