Odd One Out: Orientation Versus Where the Dot Sits
In an odd-one-out item you have 50 seconds. Six figures each show an L-shaped bracket made of three equal squares, with one small black dot inside one square. The bracket has a corner square shared by both arms, a short arm of one square, and a long arm of two squares. The figures are displayed in different rotations: figure 1 has the short arm up, figure 2 right, figure 3 down, figure 4 left, figure 5 up, and figure 6 right. The dot positions also look scattered. In figures 1–5, if you rotate the figure so that the short arm points upward and the long arm extends to the right, the dot lies in the corner square. In figure 6, after the same rotation, the dot lies in the far square of the long arm. All six have the same outline area, the same number of right angles, and the same dot size. You must choose the figure that does not belong.
1. Which figure is the odd one out, and what invariant supports your choice?
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Figure 6. Normalise every figure by rotating it until the short arm points up and the long arm points right. In figures 1–5 the dot then falls in the corner square, the square shared by both arms. In figure 6 the dot falls in the far square of the long arm. Area, right-angle count, and dot size are identical across all six, so they cannot separate any figure. Orientation also cannot separate them because the item deliberately displays different rotations. The only attribute that gives a clean five-to-one split is the dot's position relative to the bracket, and it isolates figure 6.
2. A colleague picks figure 3 because it is 'upside down'. Explain why that is a weak classification and what test you would apply instead.
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Picking figure 3 because it is upside down is weak: every figure has a different orientation, so orientation would make several figures 'odd' and does not yield a unique answer. Rotate figure 3 so the short arm is up; its dot maps to the corner square, matching figures 1, 2, 4 and 5. The correct test is landmark-based: choose the corner square as the reference, apply one normalising rotation to all six figures, then compare the dot. A figure that matches after rotation is not odd; only a figure that cannot be rotated to match is.