Apologies for those of you who are here to read about Take That. In this column’s defence, it is a continual challenge to find a funny headline with the world ‘logic’ in it.
Today’s three puzzles require logical thinking. You may have heard the first one before. Still, it is a brilliant example of the elegance of this type of conundrum.
1. The fork in the road
You are travelling to a Take That concert when you arrive at a fork in the road. Only one of the paths leads to the concert. Two people are standing there who know the way. One is a knight and the other a knave. As is well-known in logic puzzles, a knight will always tell the truth and a knave will always lie. What single question can you ask one of these people that guarantees you will know the correct path to the concert, A or B?
a) Which is the correct path?
b) Shall I choose path A?
c) What path would the other person tell me to choose?
d) Shall I choose path B?
2. The sharpest nibs in the box
Robbie, Gary and Jason work at a shop that sells pens, erasers, and pencils.
Robbie says: “Seven pens and five erasers cost the same as six pencils.”
Gary says: “Four pens and nine pencils cost the same as five erasers.”
Jason says: “Six pencils and three erasers cost the same as four pens.”
Only one is lying. Can you tell us who?
a) Robbie
b) Gary
c) Jason
3. The inevitable logic puzzle about hats
A group of people are in a room. Everyone is wearing either an orange or an indigo birthday hat. Each person can see the other people’s hats but not their own.
One of them shouts, “If you can see at least 6 orange hats and at least 6 indigo hats, raise your glass!”
Exactly 12 people raise their glasses.
How many people are in the room?
I’ll be back (for good) with the answers at 5pm UK.
UPDATE: Read the solutions here.
Never forget – NO SPOILERS. Instead, please discuss your favourite boy bands.
Today’s puzzles were suggested by Manan Khurma, the founder of Cuemath, a maths education platform that gamifies learning and claims to have taught more than 200,000 students around the world. The three puzzles (without the Take That references) are used by Cuemath to engage its pupils with logic.
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.
Thanks to Cuemath for today’s puzzles.
I’m the author of several books of maths and puzzles, and also the co-author with Ben Lyttleton of the children’s book series Football School. The latest in the Football School series is The Greatest Ever Quiz Book, out now!
I give school talks about maths and puzzles (online and in person). If your school is interested please get in touch.
