MathDB

17

Part of 2022 MIG

Problems(2)

2022 A Individual #17

Source:

4/28/2022
Jane and Jena sit at non-adjacent chairs of a four-chair circular table. In a turn, one person can move to an adjacent chair without a person. Jane moves in the first turn, and alternates with Jena afterwards. In how many ways can Jena be adjacent to Jane after nine moves?
<spanclass=′latex−bold′>(A)</span>16<spanclass=′latex−bold′>(B)</span>18<spanclass=′latex−bold′>(C)</span>32<spanclass=′latex−bold′>(D)</span>162<spanclass=′latex−bold′>(E)</span>512<span class='latex-bold'>(A) </span>16\qquad<span class='latex-bold'>(B) </span>18\qquad<span class='latex-bold'>(C) </span>32\qquad<span class='latex-bold'>(D) </span>162\qquad<span class='latex-bold'>(E) </span>512
2022 A Individual
2022 B Individual #17

Source:

4/30/2022
What is the value of (2−1)4+1(2−1)4?(\sqrt{2}-1)^4+\frac{1}{(\sqrt{2}-1)^4}?
<spanclass=′latex−bold′>(A)</span>32−162<spanclass=′latex−bold′>(B)</span>30<spanclass=′latex−bold′>(C)</span>34<spanclass=′latex−bold′>(D)</span>15+152<spanclass=′latex−bold′>(E)</span>16+162<span class='latex-bold'>(A) </span>32-16\sqrt{2}\qquad<span class='latex-bold'>(B) </span>30\qquad<span class='latex-bold'>(C) </span>34\qquad<span class='latex-bold'>(D) </span>15+15\sqrt{2}\qquad<span class='latex-bold'>(E) </span>16+16\sqrt{2}
2022 B Individual