Medium Puzzles 

Workings

Hint
The first letters of the words are: F, T, W, S, F, T, T, T, S, M.

Answers
Fluffy Tiger Whiskers Spot Felix Tom Tabby Tiddles Socks Mittens

Workings

Hint
The 4^th word begins with the letter Q.

Answers
ba-g- = badge (DE) d--ed = dazed (AZ) dia-- = diary (RY) -uo-a = quota (QT) i-de- = index (NX) -o-el = vowel (VW) -um-s = bumps (BP) py--y = pygmy (GM) g-ou- = ghoul (HL) --nal = final (FI) tra-- = track (CK) -umb- = jumbo (JO) d--ty = dusty (US)
This puzzle isn't guaranteed to have a unique answer, can you find another?

Workings

Hint
Try removing the spaces from the sequence.

Answer
1301311 or 1210121.

Reasoning
Removing spaces from the original sequence gives:

   1 23 124 1251 26127 128129

   123124125126127128129

Now adding spaces back in, in the correct place:

   123 124 125 126 127 128 129

The next few terms could be:

   130 131 132
   or
   1210 1211 1212

Add these to the end:

   123 124 125 126 127 128 129 130 131 132
   or
   123 124 125 126 127 128 129 1210 1211 1212

Remove the spaces again:

   123124125126127128129130131132
   or
   123124125126127128129121012111212

Now break the sequence into chunks of increasing size:

   1 23 124 1251 26127 128129 1301311
   or
   1 23 124 1251 26127 128129 1210121

So the missing term is 1301311 or 1210121.

Workings

Hint
The area of a circle is π x Radius².

Answers
Circle: 35.

Square: 31.

Triangle: 47.

Doughnut
The area of a circle is π x Radius².

The larger circle has diameter = 40, therefore the radius is 20, and the area is π x 20² = 400π.

The smaller circle has diameter = 20, therefore the radius is 10, and the area is π x 10² = 100π.

Therefore the shaded area is 400π – 100π = 300π ≈ 942.

Circle
The area of a circle is π x Radius².

The circle with diameter 31 has a radius of 15.5 and an area of π x 15.5² ≈ 755.

The circle with diameter 35 has a radius of 17.5 and an area of π x 17.5² ≈ 962 (closest match).

The circle with diameter 39 has a radius of 19.5 and an area of π x 19.5² ≈ 1195.

Square
The area of a square is Side x Side.

The square with side 31 has an area of 31 x 31 = 961 (closest match).

The square with side 35 has an area of 35 x 35 = 1225.

The square with side 39 has an area of 39 x 39 = 1521.

Triangle
The area of a triangle is ¹/₂ x Base x Height. Using Pythagoras' theorem it can be shown that the area of an equilateral triangle is √3 x Base² ÷ 4.

The triangle with side 39 has an area of √3 x 39 x 39 ÷ 4 ≈ 659.

The triangle with side 43 has an area of √3 x 43 x 43 ÷ 4 ≈ 801.

The triangle with side 47 has an area of √3 x 47 x 47 ÷ 4 ≈ 957 (closest match).