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!

Can ants feel pain?

Question

Carol asks: Can ants feel pain?

Answer

I went crawling around for the answer with York University’s Eleanor Drinkwater…

  • Ants can sense that they’ve been harmed and react but this is different to actually feeling pain
  • Nociception is the sensory nervous system informing the brain that you’ve been hurt, whereas pain is an unpleasant sensation with a negative emotional response
  • One can occur without the other eg. when playing sports you often don’t realise that you are injured until afterwards, or people who have lost limbs experience phantom limb pain
  • Robots can also be programmed to experience nociception without experiencing pain, for example in the video game The Sims characters will jump around if they’re burnt by fire
  • We currently know very little about insect expressions of pain, but we do know that the pain expression systems are different to those in mammals, meaning that insects are likely to experience pain in a different way to humans
  • In short, the jury is still out, so best to be nice to any ants that you may come across!

Part of the Naked Scientists Question of the Week series – you can listen to the full version here.

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?

Thick and sticky fluids

The fourth 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.

Viscosity is a property of a fluid on the molecular scale and is a measure of the strength of the internal friction between fluid particles. What this means in practice is that the thicker and stickier the fluid, the higher its viscosity.

Your task in this week’s puzzle is to order the six fluids below by their viscosity, lowest first. The answer will be posted in 2 weeks along with the next puzzle – good luck!

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

puzzle4

ANSWER

3. Air 1.81 x 10-5 [Pa s]

2. Water 8.9 x 10-4

1. Blood 3 x 10-3 

6. Honey 2-10 [Pa s]

5. Ketchup 50-100 [Pa s]

4. Peanut butter 250 [Pa s]

A mathematicians age is but a number…

The third 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.

Can you place the (extremely) famous mathematicians below in order of the year that they were born, earliest first? Bonus points for telling me what they studied.

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

birthdays_letters

b. Fermat: 1601-1665 – The French mathematician behind the infamous ‘Last Theorem’ written in the margins of his copy of Arithmetica in 1637. The theorem was finally shown to be true by Andrew Wiles 358 years later.

d. Newton: 1643-1727 – Most famous for his formulation of the Law of Gravity, but he also made significant contributions to geometry and is credited with developing calculus alongside Leibniz.

a. Euler: 1707-1783 – He worked on every almost every area of maths, but perhaps most famous for Euler’s number e=2.718… and Euler’s identity e  + 1 = 0.

c. Gauss: 1777-1855 – Like Euler, Gauss worked across all branches of maths and made significant contributions to Statistics with the Gaussian Distribution and physics with Gauss’ Flux Law.

The Tragic History of Mathematicians

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

Below are portraits of four famous mathematicians from history that have all died in tragic circumstances. Your task is to match up the mathematician with one of the following causes of death:

  • Shot in a duel
  • Pushed overboard from a ship
  • Suicide
  • Lost his mind

Bonus points for explaining the work of any of the mathematicians shown. Good luck!

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

tragic-deaths

Answer:

a. Hippasus – Pushed overboard from a ship for his discovery and subsequent proof that the square root of 2 is an irrational number (cannot be written as a fraction).

b. Cantor – Lost his mind after discovering that there are more one type of infinity. For example the positive integers (whole numbers) are countably infinite, whilst the real numbers are uncountably infinite.

c. Boltzmann – Suicide. He is most famous for the development of statistical mechanics which explains how the properties of atoms determine the physical properties of matter.

d. Galois – Shot in a duel after being involved in a ‘love triangle’. Fortunately he wrote down all of his work/thoughts the night before which now forms the basis of Galois theory.

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