Question

there are five cards on the table with positive integers written on both sides. the numbers, in order, 1, 2, 6, 7, and 15 are written on their visible sides. lizzie claims that we can flip over some cards so that both sides show arithmetic sequences, without reordering the cards. what is the smallest number of cards we must turn over to determine whether or not lizzie is correct?

Answer 1

Explanation:

Clearly, the 1st card must have 1 on both sides, as given in the question that both sides of a card are written with positive integers. Thus, the smallest number of cards we must turn over is ZERO.

Why? Because there is no A.P. with only positive integers in its progression that has the sequence 1, (...), 6. So we know for sure Lizzie is incorrect.