Patterns & Reasoning

Problem

Find shape and color repeats separately

Twelve shapes are lined up in a row. The shapes repeat square, triangle, circle, and the colors repeat red, yellow, alternating. In order: 1st red square, 2nd yellow triangle, 3rd red circle, 4th yellow square, 5th red triangle, 6th yellow circle, 7th red square, 8th is blank, 9th red circle, 10th yellow square, 11th red triangle, 12th yellow circle. Draw the shape for spot 8 and color it correctly.
red yellow ?
Operations
Your answer
How to solve
Strategy Look for a Pattern — Since shape and color repeat on different cycles, find each cycle separately, list out the positions, and read off what belongs at spot 8.
1STEP 1

Find the shape cycle

Shapes repeat square→triangle→circle every 3 spots. Spot 7 is a square, so spot 8 is a triangle.

square → triangle → circle (repeat)
2STEP 2

Find the color cycle

Colors alternate red→yellow every 2 spots — odd spots are red, even spots are yellow.

red → yellow (repeat), 8 is even
3STEP 3

Combine shape and color

Spot 8 is a triangle by shape and yellow by color — a yellow triangle.

Answer
a yellow triangle
Check — placing a yellow triangle between spot 7 (red square) and spot 9 (red circle) keeps both the shape order square-triangle-circle and the color order red-yellow-red intact.
Takeaway

Find the shape cycle and the color cycle separately, then combine them to pin down exactly what belongs in the blank.

  • Check the shape cycle (every 3) → triangle
  • Check the color cycle (every 2) → yellow
  • Combined, spot 8 is a yellow triangle
Where next?
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▶ Practice — 8 problems