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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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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All the digits from 1 to 9 are written in the grid below, one in each cell.

The product of the three digits in the first row is 12.

The product of the three digits in the second row is 112.

The product of the three digits in the first column is 216.

The product of the three digits in the second column is 12.

What is the product of the digits in the shaded diagonal?

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James tells only the truth on Mondays, Tuesdays, Wednesdays and Thursdays.

He tells only lies on all the other days.

Jane tells only the truth on Fridays, Saturdays, Sundays and Mondays.

She tells only lies on all the other days.

On one day last week, they both said, "Yesterday I told lies."

On which day of the week was that?

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There are 120 different arrangements of the five letters in the word ANGLE.

If all 120 are listed in alphabetical order starting with AEGLN and finishing with NLGEA, which position in the list does ANGLE occupy?

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Six of the squares in the diagram are to be shaded so the shaded squares make the net of a cube.

In how many different ways can this be done?

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