19.5. Given 8 objects, one of which is marked. It is required to ask 3 questions, to which only "yes" and "no" answers are given, and find out which object is marked.
19.5. Let's number the items from 0 to 7. We will ask questions about whether the selected item belongs to the groups $\{0,2,4,6\},\{0,1,4,5\}$, and $\{0,1,2,3\}$. Let $\varepsilon_{i}=0$ if the answer to the $i$-th question is "yes", and $\varepsilon_{i}=1$ otherwise. Then the selected item has the number $\varepsilon_{1}+2 \varepsilon_{2}+4 \varepsilon_{3}$.

Indeed, let's write the numbers of the items in binary: $a_{0}+a_{1} \cdot 2+a_{2} \cdot 4$, where $a_{i}=0$ or 1. Then the $k$-th question can be rephrased as: "Is $a_{k-1}$ equal to zero?"