The brainbuster

Find the solution to this brainbuster and win £200 of Amazon vouchers to spend on high-tech!

As COO, Jane is supervising the refit of the company’s new office premises. It was all going smoothly until they realised the basement datacenter’s air conditioning didn’t meet new regulations, and it will need to be refitted.

The contractors she has brought in, and IT, agree they can’t move the vents installed as it will compromise the cooling setup.

Contractors are debating optimal duct arrangements, and have pointed out that sections of ducting are cheaper if bought in sets of four. To make things worse, they can only source right-angled joints.

This is the existing vent arrangement (larger image):

Before Jane berates the contractors, she wants to know, how many possible distinct squares of ducting can they make between vents, without moving them?

(Join the dots, only drawing complete squares whose corners are at dots. Squares can overlap and reuse the same dots. Answers need only include the maximum number of possible distinct squares, though explanation is welcome.)

Only complete entry forms will be considered. Respondents with unusual answers may be asked to show their working else be excluded. A single prize will be awarded, for the best entry. The judge's decision is final.

This competition closes on Sunday 1st September 2024.