Count the number of squares in the given figure.

Solution

The figure may be labelled as shown. The simplest squares are EFRQ, MQYX, QRZY, RNSZ, LXWK, XYA1W, YZB1A1, ZSTB1, SGHT, WA1VP, A1B1UV, B1TOU and VUIJ i.e. 13 in number. The squares having two components each are AEYL, FBGZ, KA1JD and B1HCI i.e. 4 in number. The squares having four components each are MRB1W, QNTA1 XZUP and YSOV i.e. 4 in number. The squares having seven components each are AFB1K, EBHA1 LZID and YGCJ i.e. 4 in number. There is only one square i.e. MNOP composed of nine components. There is only one square i.e. ABCD composed of seventeen components. There are 13+ 4 + 4 + 4+1 + 1 = 27 squares in the figure.