MathDB

14

Part of 2022 MIG

Problems(2)

2022 A Individual #14

Source:

4/28/2022
Four coins are placed in a line. A passerby walks by and flips each coin, and stops if she ever obtains two adjacent heads. If the passerby manages to flip all four coins, how many possible head-tail combinations exist for her four flips?
<spanclass=′latex−bold′>(A)</span>4<spanclass=′latex−bold′>(B)</span>6<spanclass=′latex−bold′>(C)</span>8<spanclass=′latex−bold′>(D)</span>10<spanclass=′latex−bold′>(E)</span>12<span class='latex-bold'>(A) </span>4\qquad<span class='latex-bold'>(B) </span>6\qquad<span class='latex-bold'>(C) </span>8\qquad<span class='latex-bold'>(D) </span>10\qquad<span class='latex-bold'>(E) </span>12
2022 A Individual
2022 B Individual #14

Source:

4/30/2022
Two truth tellers and two liars are positioned in a line, where every person is distinguishable. How many ways are there to position these four people such that everyone claims that all people directly adjacent to them are liars?
<spanclass=′latex−bold′>(A)</span>4<spanclass=′latex−bold′>(B)</span>6<spanclass=′latex−bold′>(C)</span>8<spanclass=′latex−bold′>(D)</span>12<spanclass=′latex−bold′>(E)</span>16<span class='latex-bold'>(A) </span>4\qquad<span class='latex-bold'>(B) </span>6\qquad<span class='latex-bold'>(C) </span>8\qquad<span class='latex-bold'>(D) </span>12\qquad<span class='latex-bold'>(E) </span>16
2022 B Individual