A little puzzle about distributing $$$ into buying only certain types of sets.

MathBuilder · 2015-02-27T04:19:36.000Z

Earlier today I was reading this http://community.brickpicker.com/topic/11319-10221-super-star-destroyer/page-208#entry428778 and this http://community.brickpicker.com/topic/9539-400-to-spend-one-big-exclusive-or-lots-of-discount-sets/#entry259768 In particular the part about spending $700 coming from a SSD into 3.5 Red 5s. The obvious problem of the 3.5 Red 5s not being an integer reminded me about a classical problem on non-negative linear combinations of positive integers. Without giving a way the name of this classical problem yet, I will pose this question: Assume you are the winner of a BrickPicker gift card for a value up to $430 in an ideal S @ **** where there is no tax and all .99 prices are rounded to the full dollar. You can chose the value of the gift card but the condition is that you must use it all at once for the full amount and can only chose combinations of these 3 sets: 10698 LEGO