In the last week or so, there has been quite a buzz in some circles about a logic problem given to 14 year old students for the Singapore and Asian Schools Math Olympiad (SASMO) for Secondary 3 and 4 students, as follows:
Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates:
May 15 | May 16 | May 19 | |||
June 17 | June 18 | ||||
July 14 | July 16 | ||||
August 14 | August 15 | August 17 |
Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively, to which Albert and Bernard respond by saying:
Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too.
Bernard: At first I didn’t know when Cheryl’s birthday is, but now I do know.
Albert: Then I also know when Cheryl’s birthday is.
So when is Cheryl’s birthday?
This post is for those who would like to do Target puzzles with larger word counts.
I have made a list of every possible Target puzzle. There are over 2500 Targets with word counts of 100 or more (not including obscure words). Why don’t we see Targets like these, especially on weekends? Contact your newspaper and tell them what you want!
There are a number of stages experienced by many of us as year 12 students (yes, most of us, even parents, have been there at some point)…
Just chillaxing in January
Although some students are already getting started…
(The calm before the storm.)
Foreboding in February
I’m not quite sure what it’s going to be like, but it looks even bigger than I imagined.
I don’t actually know what I intend to do after school (except maybe a gap year).
Actually, why am I doing year 12 anyway?
(That’s OK. I tell students, only half-jokingly, that I still don’t know what I’m going to do when I grow up.)
When studying probability, most textbooks have questions using playing cards as the objects of interest.
Some students come from (family or cultural) backgrounds which means they have no experience of cards, which means that solving problems with playing cards is itself a problem for them.
So, here is a simple summary of the standard structure of a deck of cards.
In my last post, I gave you the problem of The Vicar, The Bishop And The Bellringers.
This problem really is very neat – an extremely clever interweaving of particular numbers and their factors. It needs only arithmetic as applied to prime factors.
I restate the problem here, at least in part to give you thinking time so you’re not looking straight at the solution…
I was told this by the father of a family from Hamilton in New Zealand, whom a friend and I met while cycling in NZ in early 1975.
I like this problem because (a) initially it looks like there is not enough information to solve it and (b) I can explain the solution to a moderately bright 12 year old.
I have since seen this or similar problems in a number of places, but I still think it is beautifully constructed, with implicit information that is nevertheless there if you can see it.
The Bellringers Problem
A bishop and her friend the vicar were both amateur but well-practised mathematicians, and often set each other problems to solve.
One day, the bishop visited the vicar. While the two were walking in the grounds of the vicarage, three bellringers passed them by.
“Why, they’re a fine bunch of bellringers!” said the bishop. “How old are they?”
“Well, I can tell you two things…” said the vicar.
“Firstly, if you multiply their ages, you get 2450.”
“Secondly, if you add their ages together, you get twice your age.”
The bishop had come prepared for such a challenge. She took pen and paper from her pocket and scribbled down a few numbers, but then looked up and said, “You haven’t given me enough information.”
The vicar added, “Oh, yes, I see. Well, I’m older than any of you.”
The bishop looked down at her scribblings and then said, “Ah! Now I know the bellringers’ ages.”
The question is: How old is the vicar?
A bit of fun this time round… I’ve made a spreadsheet to let you see your important age anniversaries in months, weeks, days, hours, minutes and seconds. When will you be (or when were you?!) one billion seconds old, or half a million hours old (a milestone I reached last year), or 2000 weeks old, or…? (See http://xkcd.com/1000/ for another view on special anniversaries.)