by Danny Roth
The players in a local football team have the numbers 1 to 22 with eleven playing and eleven in reserve in any match.
In one match, the players on the field were such that there was no sequence of three consecutive numbers among them. The same was true of the reserves. The sum of the fielded player’s numbers was also a perfect square.
All these facts remained true after a single substitution at half time but the perfect square was then higher.
What were the numbers (in increasing order) of the players in the first half of the match?