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Question (21)

QN0030848

A 2 × 12 grid requires how many 2 × 1 tiles for complete tiling?

(A) 10
(B) 11
(C) 12
(D) 24

Correct Answer: C

Explanation:

Total squares = 24, so 24 ÷ 2 = 12 tiles.

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Question (22)

QN0030849

A rectangular grid has 48 unit squares. How many 2 × 1 tiles are required to cover it completely?

(A) 22
(B) 23
(C) 24
(D) 48

Correct Answer: C

Explanation:

Number of tiles = 48 ÷ 2 = 24.

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Question (23)

QN0030850

Which of the following grids definitely has an even number of unit squares?

(A) 11 × 13
(B) 8 × 15
(C) 9 × 9
(D) 7 × 5

Correct Answer: B

Explanation:

If one dimension is even, the total number of unit squares is even.

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Question (24)

QN0030851

A 5 × 3 grid has one unit square removed. How many unit squares remain?

(A) 12
(B) 13
(C) 14
(D) 15

Correct Answer: C

Explanation:

5 × 3 = 15; removing one square leaves 14.

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Question (25)

QN0030852

In a black-and-white colouring of a grid used for tiling analysis, every 2 × 1 tile always covers

(A) two black squares
(B) two white squares
(C) one black and one white square
(D) three squares

Correct Answer: C

Explanation:

Every domino always covers one black and one white square.

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Question (26)

QN0030853

In the black-and-white method, if a region has 10 black squares and 8 white squares, the region is

(A) always tileable
(B) not tileable
(C) tileable only with rotation
(D) tileable only with square tiles

Correct Answer: B

Explanation:

Unequal numbers of black and white squares make domino tiling impossible.

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Question (27)

QN0030854

Which colouring helps in deciding whether some domino tiling problems are impossible?

(A) Red-blue colouring
(B) Black-and-white colouring
(C) Rainbow colouring
(D) Green-yellow colouring

Correct Answer: B

Explanation:

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Question (28)

QN0030855

A region contains 16 black squares and 16 white squares. Which statement is correct?

(A) It is definitely not tileable.
(B) Equal numbers are necessary but do not by themselves guarantee tiling.
(C) It is always tileable.
(D) Only triangular tiles can cover it.

Correct Answer: B

Explanation:

Equal numbers of black and white squares are necessary, but additional conditions may still prevent tiling.

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Question (29)

QN0030856

Which of the following regular polygons can tile the entire plane by itself?

(A) Regular pentagon
(B) Regular hexagon
(C) Regular heptagon
(D) Regular nonagon

Correct Answer: B

Explanation:

Regular hexagons tile the plane without gaps or overlaps.

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Question (30)

QN0030857

Which of the following sets contains only regular polygons that can tile the entire plane individually?

(A) Square, regular pentagon, regular hexagon
(B) Equilateral triangle, square, regular hexagon
(C) Square, regular octagon, regular pentagon
(D) Equilateral triangle, regular pentagon, regular octagon

Correct Answer: B

Explanation:

Equilateral triangles, squares, and regular hexagons are the only regular polygons that individually tile the plane.

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Question (21)

A 2 × 12 grid requires how many 2 × 1 tiles for complete tiling?

Explanation:

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Question (22)

A rectangular grid has 48 unit squares. How many 2 × 1 tiles are required to cover it completely?

Explanation:

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Question (23)

Which of the following grids definitely has an even number of unit squares?

Explanation:

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Question (24)

A 5 × 3 grid has one unit square removed. How many unit squares remain?

Explanation:

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Question (25)

In a black-and-white colouring of a grid used for tiling analysis, every 2 × 1 tile always covers

Explanation:

Link:

Question (26)

In the black-and-white method, if a region has 10 black squares and 8 white squares, the region is

Explanation:

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Question (27)

Which colouring helps in deciding whether some domino tiling problems are impossible?

Explanation:

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Question (28)

A region contains 16 black squares and 16 white squares. Which statement is correct?

Explanation:

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Question (29)

Which of the following regular polygons can tile the entire plane by itself?

Explanation:

Link:

Question (30)

Which of the following sets contains only regular polygons that can tile the entire plane individually?

Explanation:

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