Brain Out Level 147

Overview

A complex line figure combines a pentagon outline with overlapping diagonal lines, and the prompt asks for the total number of triangles inside it. The challenge is that small triangles combine into larger ones, and a quick glance usually misses several. The correct count for this drawn figure is 7, which you enter into the input field.
The overlapping pentagon and diagonals create many closed regions, some three-sided and some four-sided, so a quick glance tends to miss the composite triangles.

• Difficulty: Hard
• Estimated moves: 1

Step-by-Step Solution

1. Study the pentagon and the crossing diagonals. Ignore the outer outline and focus on the closed three-sided shapes formed wherever three lines meet.
2. Count the smallest individual triangles first, marking each one mentally so you do not count it twice.
3. Then check whether pairs or groups of those small pieces join into larger triangles bounded by the drawn lines.
4. Combine the small and larger triangle counts, making sure every counted shape has three straight sides and a fully closed boundary.
5. Enter 7 in the answer field and confirm. The level accepts 7 once the triangle count matches the figure.

Mark the smallest closed triangles first and keep a mental list so none is counted twice, then check whether neighboring small regions join into larger triangles bounded by the drawn lines. Exclude any region with four sides from the tally, and only count shapes with three straight, fully closed edges. Combine the small and composite counts, enter 7 in the field, and confirm. If your first count differs, rescan for larger triangles that span several small pieces rather than recounting the tiny ones.

Go around the figure once for the small triangles and once more for the composites, marking each counted shape so the overlap between neighboring triangles does not get tallied twice. Four-sided regions formed by the crossing lines must be left out, and when your second sweep adds no new larger triangle, the settled count 7 is ready to enter.

Strategy & Reasoning

Counting shapes in a dense line drawing requires a systematic sweep rather than a first impression. Small regions can merge into bigger triangles, while some enclosed areas are quadrilaterals and must not be counted. Listing the elementary triangles first, then checking composite ones, keeps the tally consistent and avoids double counting. The settled answer for this particular overlap pattern is 7, and the field expects that single total. Dense line-figure counting needs a systematic sweep: elementary regions first, composites second, so overlaps do not double up. The four-sided areas in the network are the main source of miscounting, and the settled total for this overlap pattern is 7, which the field expects as one number.

Tips & Common Mistakes

• Count closed three-sided figures only; four-sided regions in the network do not qualify.
• Look for larger triangles made of smaller pieces, not just the obvious tiny ones.
• Enter 7, not the number of small triangles you spot first; the composite shapes change the total.