Month: March 2020

Ben Sparks gives instructions to do some disease modelling on Geogebra – so you can see the maths behind the government advice to “flatten the curve”. Geogebra is available here. When you try and recreate the applet, don’t worry if the first three numbers appear as sliders, it will still work fine.

Also, see the message below from the Think Maths website we have enjoyed in the past:

“Matt Parker has launched Matt Parker’s Maths Puzzles! Once a week we can now look forward to a puzzle video from Matt on his Stand-Up Maths YouTube Channel.

Each week Matt will give us a puzzle and pose a question. Viewers can submit their solution to that question online to receive points and appear in a puzzle participants league table. 

Matt will be awarding hilarious virtual prizes when participants reach particular point milestones.

The first puzzle video is here. Submit your answer here: www.think-maths.co.uk/table-puzzle

We aim for puzzle videos to be released on a Wednesday afternoon UK time, with the deadline for submissions the Tuesday of the following week at 11:59pm UK time. 

Sign up to recieve an alert email when puzzle videos come out here: https://www.think-maths.co.uk/puzzles-sign-up

On Fridays we will post a solution video to the previous week’s puzzle and the updated league table on this page: www.think-maths.co.uk/maths-puzzles“

Take care everyone.

Here are a couple of age puzzles from David Pleacher’s great site. Answers are on there too.

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During a recent census, a man told the census taker that he had 3 children.
When asked their ages, he replied, “The product of their ages is 72.”
“The sum of their ages is the same as my house number.”
The census taker ran to the door and looked at the house number.
“I still can’t tell,” she complained.
“Oh, that’s right. I forgot to tell you that the oldest one likes apple pie.”
The census taker promptly wrote down the ages of the three children.
How old are they?

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Edie and Dave were talking when they saw three people coming toward them.
“I wonder how old they are,” said Edie.
Dave replied, “I know them!
The product of their ages is 2,450 and the sum of their ages is twice your age.”
“That’s all well and good,” said Edie, “but I need more information.”
“Oh yes,” said Dave.
“Well, I am older than any of the three.”
“Now, I can figure their ages,” said Edie.

How old are the three?

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In case they were too easy here is a fiendish one to try by John H. Conway.

Last night I sat behind two wizards on a bus, and overheard the following: A: “I have a positive integral number of children, whose ages are positive integers, the sum of which is the number of this bus, while the product is my own age.” B: “How interesting! Perhaps if you told me your age and the number of your children, I could work out their individual ages?” A: “No.” B: “Aha! AT LAST I know how old you are!” Now what was the number of the bus?

Here is a paper which discusses the puzzle and solution.

A half term trip to Bletchley Park inspired the following activity …

Task 1

Go to
https://billtuttememorial.org.uk/codebreaking/teleprinter-code/

Read about teleprinter code and the rules of addition.

Task 2

In the alphabet in the link above, I and N are incorrect.

Can you use their addition table to work out what I and N should be? Remember that same symbols added make a dot, and different symbols make a cross.

Here is an addition table in alphabetical order.

Task 3

Code HELLO with the key ANQPC.
How would you get back to HELLO?

Solution here

Task 4

Read about the Tiltman break here

Task 5

Try it out for yourself!!

Above are two messages sent with the same key. One has been abbreviated after the operator was asked to send it again. Your crib is that it starts MESSAGE NUMBER (of course with a 9 in the middle!). You also know it is a weather report.  

If you add together the two messages letter by letter (using the table) you will end up with the two messages added together, because for:

Message1 +key + Message2 + key

the keys will cancel out and it will be Message1 + Message2

So if you can guess it starts MESSAGE9NUMBER then you can add this to the sum of the two messages and as they start to be different you can work out each one …