Non-Pool
Topic: #puzzlefortoday

A shameless reposting of BBC Radio 4 Today Programme's #puzzlefortoday to see if anyone else enjoys these as much as I do...



Puzzle No. 331 – Wednesday 10 October

One year, there were exactly four Tuesdays and exactly four Fridays in October. On what day of the week did Halloween, October 31st, fall that year?

Today’s #PuzzleForToday has been set by the University of Cambridge’s NRICH project (nrich.maths.org), in collaboration with the UKMT.

http://www.bbc.co.uk/programmes/articles/508GV9s2wd2GM0dCknXRT1w/puzzle-for-today

Yesterday's answer - I've got to admit I didn't get this one, and I'm not sure I even understand the printed answer, but a friend of mine got it, so fair does to him...

THE ANSWER

Puzzle No. 331 – Wednesday 10 October
One year, there were exactly four Tuesdays and exactly four Fridays in October. On what day of the week did Halloween, October 31st, fall that year?

Today’s #PuzzleForToday has been set by the University of Cambridge’s NRICH project (nrich.maths.org), in collaboration with the UKMT




October has 31 days so, in any year, in October there will be three days of the week which occur five times and four days which occur four times.

As there were exactly four Tuesdays and exactly four Fridays, there could not have been five Wednesdays or five Thursdays, so the days which occurred five times were Saturday, Sunday and Monday.

Therefore October 1st must have been a Saturday, which means that October 31st was a Monday.

Today's question...

Puzzle No. 332 – Thursday 11 October
The precious emerald of Copan was first discovered in 25BC but it went missing 50 years later and has never been since. What year did the emerald disappear?

Today’s #PuzzleForToday has been set by the Spectrum Secret Agency Entrance Exam – as featured in Lauren Child’s and Marcus du Sautoy's novels about the code breaking child genius Ruby Redfort.

http://www.bbc.co.uk/programmes/articles/14931n1nNxgbc2w2L7Y3P9X/puzzle-for-today

26AD

THE ANSWER

Puzzle No. 332 – Thursday 11 October
The precious emerald of Copan was first discovered in 25BC but it went missing 50 years later and has never been since. What year did the emerald disappear?

Today’s #PuzzleForToday has been set by the Spectrum Secret Agency Entrance Exam – as featured in Lauren Child’s and Marcus du Sautoy's novels about the code breaking child genius Ruby Redfort.


Most people’s response is 25AD but that is incorrect! There was no year 0 so actually the emerald went missing in 26AD.

Puzzle No. 333 – Friday 12 October
Tomorrow sees the deciding game of rugby league’s 2018 Super League with the Grand Final between Warrington Wolves and Wigan Warriors. For the following puzzle, answer what immediately comes to mind! During half-time for the final, you buy a souvenir t-shirt and a bottle of water that costs £11 altogether. The souvenir t-shirt costs £10 more than the bottle of water. How much does the bottle of water cost?

Today’s #PuzzleForToday has been set by Bobby Seagull, a school Maths teacher and Cambridge University Doctorate student.

http://www.bbc.co.uk/programmes/articles/4w0g9HPTv7sgt9gSLjmrjt/puzzle-for-today

THE ANSWER

Puzzle No. 333 – Friday 12 October
Tomorrow sees the deciding game of rugby league’s 2018 Super League with the Grand Final between Warrington Wolves and Wigan Warriors. For the following puzzle, answer what immediately comes to mind! During half-time for the final, you buy a souvenir t-shirt and a bottle of water that costs £11 altogether. The souvenir t-shirt costs £10 more than the bottle of water. How much does the bottle of water cost?

Today’s #PuzzleForToday has been set by Bobby Seagull, a school Maths teacher and Cambridge University Doctorate student.


This is similar to a famous "bat and ball" problem set by Nobel prize winning Economist Daniel Kahneman, where 50% of Harvard, MIT and Princeton students gave the intuitive, but incorrect answer. In our question, you may have been tempted to say the bottle of water costs £1. However if this were the case, the souvenir t-shirt would cost £11 (£10 more) and this would cost £12 in total, which is incorrect. The correct solution is the bottle of water is £0.50 and souvenir t-shirt is £10.50.



The next puzzle will appear on Monday.

Puzzle No. 334 – Monday 15 October
There are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes have been incorrectly labeled such that no label identifies the actual contents of the box it labels. Opening just one box, and without looking inside the box, you take out one piece of fruit. By looking at the fruit, how can you immediately label all of the boxes correctly?

Today’s #PuzzleForToday has been set by Dr. Elon Correa Lecturer in Mathematics and Statistics, University of Salford.


http://www.bbc.co.uk/programmes/articles/2F0bDpN8r5WYGl9TG2KgPgy/puzzle-for-today

THE ANSWER

Puzzle No. 334 – Monday 15 October
There are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes have been incorrectly labeled such that no label identifies the actual contents of the box it labels. Opening just one box, and without looking inside the box, you take out one piece of fruit. By looking at the fruit, how can you immediately label all of the boxes correctly?

Today’s #PuzzleForToday has been set by Dr. Elon Correa Lecturer in Mathematics and Statistics, University of Salford.

Open the box that is labeled "Apples and Oranges". You know that since none of the labels are correct, the box must either contain only apples, or only oranges. Suppose that you remove an apple from that box. Therefore, that box must be the "Apples Only" box. One of the two remaining boxes must be the "Oranges Only" box. However, one is labeled "Apples Only", and the other is labeled "Oranges Only". Therefore, the one labeled "Apples Only" is the box that contains only oranges, and the box labeled "Oranges Only" is the box that contains both kinds of fruit.

Puzzle No. 335 – Tuesday 16 October
The BBC recently reported that life expectancy of men is about 79 years and that of women is about 83 years. These should be increasing by 2 months per year, but this has stopped (https://www.bbc.co.uk/news/health-45638646). If we can start increasing life expectancy by 2 months per year again, what is the life expectancy of someone born today?

Today’s #PuzzleForToday has been set by Dr Shaun Fitzgerald, Director of The Royal Institution

THE ANSWER

Puzzle No. 335 – Tuesday 16 October
The BBC recently reported that life expectancy of men is about 79 years and that of women is about 83 years. These should be increasing by 2 months per year, but this has stopped (https://www.bbc.co.uk/news/health-45638646). If we can start increasing life expectancy by 2 months per year again, what is the life expectancy of someone born today?

Today’s #PuzzleForToday has been set by Dr Shaun Fitzgerald, Director of The Royal Institution

Well, if you are a male and are 79 today then your life expectancy is ... 79. Watch out! We know the life expectancy of someone born today can’t be 79+79*2/12=92.17years because at that age, your life expectancy will have increased to 79+92.17*2/12 = 94.36. And so on.

The best way to solve this is by saying let life expectancy be y so that

y=79+y*2/12 for men

Solving this, we get y=94.8 (i.e. about 95) years for men. Using the same approach, we find that the life expectancy of a girl born today would be 99.6, i.e. about 100 years. Lots of letters from the monarch being written!

Puzzle No. 336 – Wednesday 17 October
The Today Programme presenters all take the same amount of sugar in their morning coffees. John only has a foot-high cone of sugar standing on his desk. He slices out the middle 4 inches of sugar and gives it to Nick. He is left with just enough sugar to make three cups of coffee for Martha, Michal and Justin, but not one for himself. Has Nick got enough sugar to make his own coffee?

Today’s #PuzzleForToday has been set by the School of Mathematics and Statistics at the University of Sheffield.