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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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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Two identical rulers and placed together, as shown.

Each ruler is exactly 10cm long and is marked in centimetres from 0 to 10.

The 3cm mark on each ruler is aligned with the 4cm mark on the other.

The overall length is L cm. What is the value of L?

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An amount of money is to be divided equally between a group of children.

If each child was to receive 60p, then £2.10 would be left over.

If there was 20p more than this amount of money, then there would be enough for each child to receive 70p.

How many children are there in the group?

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Suppose that e, i, n and t represent different positive whole numbers,

n + i + n + e = 9, t + e + n = 10 and i = 1.

What is t?

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The area of a rectangle is 120 cm^{2}, the perimeter of the rectangle is 46 cm.

What is the length of the diagonal of the rectangle?

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