Today’s three puzzles are written by Barry R Clarke, author of Mensa’s bestselling book of logic puzzles. Mensa is the society for people with high IQs, which it defines as those who score in the top 2 per cent of intelligence tests.

If you breeze through these puzzles, consider yourself a clever clogs!

1. Switched on

Three switches control three lightbulbs, such that each switch controls only one bulb, and each bulb is controlled by only one switch. Only one of the following statements is true.

Switch 1: ‘Controls bulb B’.

Switch 2: ‘Controls bulb A or C’.

Switch 3: ‘Controls bulb A or B’.

Can you match the switches to the bulbs?

2. Distance learning

Every afternoon, Jogger Jane runs from her home (left) to the school (right). Each of the four straight roads is 1km long and each of the four curved ones is 1.5km. She always runs more than 3km, and in doing so, she never passes along the same road twice. Not all roads are necessarily used in a single run, she can pass by her home, and once she reaches the school her run ends.

How many different routes can she choose from? (Hint: it’s more than 10.)

3. Musical chairs

Six chairs numbered 1 to 6 are arranged sequentially in a circle for a game of musical chairs. When the music stops, six bottoms park themselves on six chairs, each chair being occupied by one person only. When seated, the players face inwards and the person whose birthday it is manages to sit in chair 1. The positions in the circle are as follows.

(1) Malcolm, who does not have the birthday, sits immediately to the right of Sally, who is not opposite the birthday person.

(2) Jennifer does not sit next to Uri.

(3) Nat is the first to sit down.

(4) Victor sits two places to the right of Jennifer.

(5) Uri sits at least two places from the birthday person.

Whose birthday is it?

Barry R Clarke, the author of these puzzles, is a veteran creator of logical conundrums, who as well as writing for Mensa, has published thousands of puzzles in UK national newspapers and magazines over the last four decades. These teasers are adapted from his book Mathematical Conundrums, which came out last week.

Usually, I reveal the answers to the puzzles at 5pm UK, which is ten hours after I set the questions.

Today, however, I’m trialling a new format, in which the solutions are posted AT THE SAME TIME. If you want to read the solution now, please click the link here.

I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

I give school talks about maths and puzzles (online and in person). If your school is interested please get in touch.