Christmas Stamps

This Christmas themed puzzle was featured on BBC Radio 4’s Today programme as the 375th ‘Puzzle for Today‘. You can listen to the broadcast here at 48:55.

Christmas stamps are sold with the following values 16p, 17p, 23p, 24p, 39p and 40p. You want to send a present which has a postage cost of £1.00. How many stamps do you need to buy to make the exact amount?

Send your answers to @tomrocksmaths on Facebook, Twitter, Instagram, YouTube, or using the contact form on my website. The solution will be posted with the next puzzle.

Merry Christmas!

Tom Rocks Maths S02 E01

Tom Rocks Maths is back on Oxide – Oxford University’s student radio station – for a second season. The old favourites return with the weekly puzzle, Funbers and Equations Stripped. Plus, the new Millennium Problems segment where I tell you everything that you need to know about the seven greatest unsolved problems in the world of maths, each worth a cool $1 million. And not to forget the usual selection of awesome music from artists such as Rise Against, Panic at the Disco, Thirty Seconds to Mars – and for one week only – Taylor Swift. This is maths, but not as you know it…

Cannibals and hats

Time for the next puzzle in the new feature from Tom Rocks Maths – check out the question below and send your answers to @tomrocksmaths on Facebook, Twitter, Instagram or via the contact form on my website. The answer to the last puzzle can be found here.

You are walking through the jungle with two friends when all of a sudden you are attacked by a group of cannibals. Fortunately, they do not eat you straightaway, but instead devise a puzzle that you must solve to avoid being eaten. The setup is as follows:

  • You are each tied to a pole such that you can only see forwards. The poles are placed in a line such that the person at the back can see the two people in front of them, the person in the middle can see one person in front of them, and the person at the front cannot see anyone else. See diagram below.

Screen Shot 2018-09-19 at 13.25.56

  • The cannibals produce five hats: 3 are black and 2 are white. You are all then blindfolded and a hat is placed on each persons head at random. The other two hats are hidden.
  • The blindfolds are removed and you are told that you will be set free provided that one of the group can correctly guess the colour of the hat that they are wearing. An incorrect guess will cause you all to be eaten.
  • The person at the back says that they do not know the colour of their hat. The person in the middle says that they also do not now the colour of their hat. Finally, the person at the front says that they DO know the colour of their hat.

The questions is: what colour hat is the person at the front wearing and how did they know the answer?

The answer will be posted in a few weeks along with the next puzzle – good luck!

Crossing the desert

The fifth puzzle in the new feature from Tom Rocks Maths – check out the question below and send your answers to @tomrocksmaths on TwitterFacebook, Instagram or via the contact form on my website. The answer to the last puzzle can be found here.

You are responsible for driving an important person across the desert, but the cars that you have been given can only hold enough petrol to cover half of the distance. Being a desert, there are of course no petrol stations along the way. However, you have access to as many cars as you need and can transfer petrol between them.

What is the minimum number of cars that you will need and how can you complete the journey?

WARNING: answer below so scroll slowly to avoid revealing it accidentally.

 

ANSWER

The minimum number of cars required is 4. The journey can be split up as follows.

  • All four cars travel 1/4 of the distance across the desert, each using up one half of a tank.
  • Two of the cars are then emptied leaving two cars remaining, each with a full tank.
  • The two cars travel a further 1/4 of the distance, reaching half-way across the desert, each with one half of a tank remaining.
  • One car is then emptied, leaving one car remaining with a full tank.
  • The final car drives the remaining half of the distance across the desert using the full tank.

Screen Shot 2018-09-19 at 13.43.54

BONUS

How many cars do you need if a full tank of petrol allows each car to travel 1/3 of the distance across the desert? What about if a full tank only reaches 1/4 of the way across? Finally, what is the general rule for the number of cars needed to cross the desert when a full tank of petrol takes you 1/n of the total distance?

Tom Rocks Maths Episode 04

The fourth and final episode of Tom Rocks Maths this term on Oxide – Oxford University’s student radio station. Featuring my favourite shapes, cannibals with a hat fetish, the golden ratio and the weekly maths puzzle for you to solve. Plus, music from Foo Fighters, Green Day and Sum 41…

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