Completion of Incomplete Pattern Questions and Answers

Answer: B

The figure is generated by pattern Q.

The wide figure is three copies of one square tile placed side by side. Comparing that tile with the four candidates cell by cell, Q matches it everywhere.

Each of the others differs from the tile in one region: P has a different arrangement in its centre, R in its top right corner, and S in its bottom left corner, where it shows a block shape that never appears in the figure. Checking the corners and the centre first is the quick way to separate near-identical patterns like these.

Answer: B

The top view is Q.

The profile shows the hill rising steeply on the near side (summit at about 0.22 km from the origin) and sloping gently away beyond it. Seen from above, each horizontal cross-section becomes an oval. Near the summit they are small and sit close to the origin end. Lower down they grow, but their near edges stay close together, because the near slope is steep, while their far edges spread out, because the far slope is gentle.

Q shows exactly this: the smallest ovals near the origin end and the outlines crowded on the left and spread out on the right. P puts the summit on the far side, R draws concentric ovals for a symmetric hill, and S does not crowd the outlines towards the origin side.

Answer: B

The top view is Q.

The hill rises steeply on the side near 0 km and falls gently on the far side, with its summit at about 0.22 km. The cross-sections higher up the hill are smaller ovals, and they are centred close to the summit, near the 0 km end. Seen from above, the nested ovals therefore crowd together close to the 0 km mark, where the slope is steep, and spread out on the far side, where the slope is gentle.

Q shows exactly this: the smallest ovals sit near the left, close to 0 km. P puts the summit at the far end, as if the gentle slope faced 0 km. R has evenly spaced, concentric ovals, which would describe a symmetric hill. S does not shift the ovals steadily in one direction.

Answer: B

The missing square is number 2: double arrow at the top, PP on the left, C on the right and S at the bottom.

Count each symbol in the squares. Figure 1 has S, C, P and one arrow, each once. Figure 2 has P doubled (PP). Figure 4 has the arrow doubled and C doubled. Figure 5 has S doubled. Each step adds one repeat to one symbol, in the order P, arrow, C, S, so figure 3 has PP and a double arrow, with a single C and S.

Positions turn 90 degrees clockwise at every step: in figure 1 the order from the top is S, P, arrow, C, and in figure 2 it is C, S, PP, arrow. Rotating figure 2 once more puts the double arrow at the top, then C on the right, S at the bottom and PP on the left. Check: turning this once more gives figure 4, which has PP at the top and the arrows on the right, as printed.

Option 1 has the symbols in the wrong places; option 3 has CC; option 4 has C and S swapped.

Answer: A

The blank is filled by ←↑.

Read each row as three figures of two arrows. Within every row, the first arrows follow the pattern same, same, reversed: up, up, down in row 1 and down, down, up in row 2. So row 3, with left in the first figure and right in the third, needs left in the middle.

The second arrows follow the pattern given, reversed, same: down, up, up in row 1 and right, left, left in row 2. So row 3, with down first and up third, needs up in the middle.

That gives left then up. The other figures get one arrow wrong: left-down repeats the first figure, and right-up and right-down break the first-arrow pattern.

Answer: C

The set that works is (C).

In each set, two pieces carry square corners at the top (the left piece the top-left corner, the middle piece the top-right corner) and the large piece has a flat bottom and two square lower corners, so together they can make a square. The pointed lower end of the left piece fits the V-shaped notch in the top edge of the large piece, and the peak of the large piece fits under the inverted V of the middle piece.

The hole comes from curved notches. In (C) each of the three pieces has a curved notch on an inner edge, and when the pieces are fitted together the three notches meet near the centre to close one round hole.

(D) has no curved notch on any piece, so it cannot leave a round hole. In (A) the middle piece has no notch, and the notch on the large piece is cut beside its peak rather than at the inner corner, so the curved edges do not come together as one circle. In (B) the third piece is a four-sided piece with no inverted V, so it cannot fit over the peak of the large piece and the pieces do not form a square.

Answer: B

The missing figure is (B), a circle inside a square.

In each box the inner shape becomes the outer shape of the next box. The first box has a triangle inside a pentagon; the second has that triangle as its outer shape, with a square inside. So the third box must have the square as its outer shape. The fourth box is a pentagon inside a circle, so the circle must be the inner shape of the third box: a circle inside a square.

Option (A) has a circle outside, (C) a pentagon outside and (D) a triangle outside, so none of them continues the chain from the square.

Answer: B

The missing square is (B), a plain inverted triangle.

Every row and every column holds one triangle with a circle inside, one triangle with stems at top and bottom, and one plain triangle, and each row has exactly one inverted triangle.

The middle row already has a stemmed upright triangle and an upright triangle with a circle, so it needs a plain triangle, and since the row has no inverted triangle yet, it must be inverted. The middle column confirms it: it has a stemmed triangle and a circled triangle, so it also needs the plain one.

(A) adds a second stemmed triangle and (C) a second circled one to the row, while (D) is plain but upright, leaving the row without an inverted triangle.