Welcome to Ian’s Friday Puzzle! Dust off those Friday cobwebs with a little manipulation of the old grey matter. Perplexing puzzles, logical, illogical, and sometimes just plain stupid. Be prepared to be bewildered, befuddled and bedazzled!

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Lynne: “Jane is innocent”

George: “Tim is guilty”

Jane: “George is guilty”

Tim: “Lynne is innocent”

Only the guilty person is lying; all the others are telling the truth.

Who is guilty?

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The difference between ^{1}/_{4} of a certain number and ^{1}/_{5} of the same number is 3.

What is that number?

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Find the positive integer, *x*, that satisfies the equation

√3 + √12 + √27 = √*x*

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The five equally sized rectangles are placed inside a square as shown.

The square has a side length of 24 cm.

What is the area of one rectangle?

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The three rectangles below all have the same area.

What is the value of *x* + *y*?

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The largest of four different real numbers is* x*.

When the numbers are summed in pairs, the four largest sums are 13, 12, 10 and 9.

What are the possible values of *x*?

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The areas of three of the faces of a cuboid are 24 cm^{2}, 18 cm^{2} and 12 cm^{2}.

What is the volume of the cuboid?

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A square lies on a circle such that one edge passes through its centre, and two vertices lie on the circumference, as shown.

The circle has a radius of 1 cm.

What is the area of the square?

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A record is shaded as shown. It has no hole!

The radius of the label (white) is a third the radius of the record.

What is the ratio of the black shaded area to the area of the label (white area)?

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In the sequence which begins 2, 3, 5, 10, … each number after the second is the sum of all the previous numbers in the sequence. What is the 10^{th} number in the sequence?

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