Embedded Shapes

Visual Processing intelligence (Gv) is a type of thinking that requires perceiving or processing visual stimuli, forms, or patterns. It is a major function of the right hemisphere of the brain, sometimes known as the “visual hemisphere. While our left hemisphere is specialized for linear and numerical reasoning, as well as language functions such as grammar and vocabulary, the right hemisphere is specialized for visual and spatial processing.

There are many brain teasers that use of visual thinking. Here geometrical figures (triangles, rectangles) have embedded within them a number of similar smaller figures (triangles, rectangles). The challenge is to count how many such figures there are in total. The solution strategy calls for visualizing how parts can be assembled to form wholes (a typical right-hemispheric function). Such puzzles are, thus, exercises in “whole-part” thinking.

Answer: 15 rectangles

Stand alone rectangles:

(1) 1
(2) 2
(3) 3
(4) 4
(5) 5
(6) 6
(7) 7
(8) 8

Assembled rectangles:

(9) 1+2
(10) 1+2+3
(11) 1+2+3+4
(12) 1+2+3+4+5
(13) 1+2+3+4+5+6
(14) 1+2+3+4+5+6+7
(15) 1+2+3+4+5+6+7+8

Answer: 18 triangles

Stand-alone triangles
(1) 1
(2) 2
(3) 4
(4) 5
(5) 6
(6) 7
(7) 8
(8) 9

Assembled triangles
(9) 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 (large triangle)
(10) 1 + 2 + 3 + 4
(11) 2 + 5
(12) 2 + 5 + 6
(13) 3 + 7
(14) 4 + 8
(15) 4 + 8 + 9
(16) 5 + 7 + 8
(17) 5 + 7
(18) 7 + 8