What impact does sugar have on thinking skills like learning, problem solving, remembering, etc.?

Significant impact: Without sugar (in this case, glucose): your brain isn’t able to do any of those things. You’d go into hypoglycemic coma. The brain preferentially uses glucose. In a state of prolonged fasting, when glucose is scarce, the brain switches to “ketone bodies” made from other precursors, but then immediately switches back to glucose when it becomes available again.

Blood sugar: Hypergylcemia (really high blood sugars) can cause cognitive impairment. On the other hand acute hypoglycemia (really low blood sugars) can also impair cognition.