Initial stock of toffees

Work backwards from the 5th child:

Let $S_k$ be the stock before treating the $k$-th child. When stock $S$ is given, remaining stock is $\frac{S}{2} - 1$. Hence, $S_{\text{prev}} = 2(S_{\text{curr}} + 1)$.

• After 5th child, stock $= 0 \implies S_5 = 2(0 + 1) = 2$.
• Before 4th child: $S_4 = 2(2 + 1) = 6$.
• Before 3rd child: $S_3 = 2(6 + 1) = 14$.
• Before 2nd child: $S_2 = 2(14 + 1) = 30$.
• Before 1st child: $S_1 = 2(30 + 1) = 62$.

Initial stock of toffees was 62.