Refer to the following number and symbol series and answer the question.…

Concept. A condition of the form "immediately preceded by A and immediately followed by B" is a fixed three-element window test: for a target element, the neighbour one step to its left must belong to category A and the neighbour one step to its right must belong to category B, and both halves must hold on the same window at the same time. The stated counting order fixes the two directions — when counting runs from left to right, "preceded by" always means the left neighbour and "followed by" always means the right neighbour. The method therefore has two stages: first label every element of the series by category, then slide the window along the series and keep only those targets whose two neighbours match the two required categories.

Application. Here the window to be matched is symbol - symbol - number: the target itself must be a symbol, the neighbour on its left must also be a symbol, and the neighbour on its right must be a number.

1. Label the twenty-one elements from the left. Numbers stand at positions 1, 3, 4, 8, 9 and 20, carrying the values 1, 4, 6, 5, 1 and 1; the remaining fifteen positions all carry symbols.

2. Drop every symbol that has a number on its immediate left, because it already fails the "preceded by another symbol" half: ^ at position 2 (after 1), * at position 5 (after 6), & at position 10 (after 1) and & at position 21 (after 1).

3. Eleven symbols survive that first half. For each of them, test the element on the immediate right against the "followed by a number" half.

Two windows clear both halves: * at position 7, which carries ? on its left and the number 5 on its right, and % at position 19, which carries ^ on its left and the number 1 on its right.

Cross-check. Scan the series once more for a different feature: every place where a symbol is immediately followed by a number. There are three such places - ^ at position 2 (followed by 4), * at position 7 (followed by 5) and % at position 19 (followed by 1). Now apply the other half to these three: ^ at position 2 has the number 1 on its left, so it drops out, while * at position 7 has ? on its left and % at position 19 has ^ on its left. Two survive, which matches the count reached above.

Where the near misses come from:

• ? at position 6 has a symbol on its left but another symbol, *, on its right, so a symbol buried inside a long symbol block meets only the first half.

• ^ at position 2 is followed by the number 4 but is preceded by the number 1, so meeting only the "followed by" half is not enough.

• & at position 21 sits at the extreme right with the number 1 before it and no element after it at all, so the "followed by a number" half cannot be met.

Result. Two symbols of the series, * at position 7 and % at position 19, satisfy both halves of the condition.