The spaces P, Q and R have to be shaded by three different colours definitely (since each of these three spaces lies adjacent to the other two). Now, in order that no two adjacent spaces be shaded by the same colour, the spaces T, U and S must be shaded with the colours of the spaces P, Q and R respectively. Also the spaces X, V and W must be shaded with the colours of the spaces S, T and U respectively i.e. with the colours of the spaces R, P and Q respectively. Thus, minimum three colour pencils are required.
The horizontal lines are AK, BJ, CI, DH and EG i.e. 5 in number. The vertical lines are AE, LF and KG i.e. 3 in number. The slanting lines are LC, CF, FI, LI, EK and AG i.e. 6 in number. Thus, there are 5 + 3 + 6 = 14 straight lines in the figure.
The simplest triangles are AJF, FBG, HDI, GCH and JEI i.e 5 in number. The triangles composed of the three components each are AIC, FCE, ADG, EBH and DJB i.e 5 in number. Thus, there are 5 + 5 = 10 triangles in the given figure.
The simplest triangles are AKI, AIL, EKD, LFB, DJC, DKJ, KIJ, ILJ, JLB, BJC, DHC and BCG i.e. 12 in number. The triangles composed of two components each are AKJ, ALJ, AKL, ADJ, AJB and DBC i.e. 6 in number. The triangles composed of the three components each are ADC and ABC i.e. 2 in number. There is only one triangle i.e. ADB composed of four components. Thus, there are 12 + 6 + 2 + 1 = 21 triangles in the figure.