Apparently it’s the longest international land border in the world.
Ok, I’ll suggest a starting place - 5000 miles. About 4000 between North America and Canada and a further 1000 between Canada and Alaska.
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Good estimates Bobby.
Round numbers are 4,000 east/west as you quoted. Probably closer to 1,500 north/south with Alaska. ( this is the section that a few people ‘miss’ !!)
Total c. 5525 miles.
Well done Bobby.
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1500 miles on the Canada/Alaska border? Wow. I thought it was probably 600 to be honest miles but guessed 1000 miles because “Alaska is always bigger than you think”.
Apparently it’s even bigger than even bigger than you think!
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Very true ! I’ve seen claims that it’s bigger than Europe.
I guessed 4,000 but I forgot about the Alaskan border
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Join the ‘Club’ Ravvie.
i did the same initially ! even though i have driven from Prince Rupert to Dawson City and crossed the border at Hyder, Carcross, NW of Whitehorse, and west from Dawson to Chicken.
Anybody know why it’s called Chicken ?
O or A?
Apparently this GCSE Maths question left many students furious as it was also a practice question for A-level, so they considered it unfairly difficult. Each octagon has side length = a.
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Nice Teaser Ravvie.
Let’s try P=4
ie Area = 4(2 + sqrt(2))a^2
You could easily over-count the number of little triangles. (well, I nearly did !!)
My working-out …
Of course you need to recognise that each side of a regular octagon turns 45 deg at each external angle and hence the “star-shaped” is formed by right-angled-isosceles triangles.
But only four such “stars” lie outside the perimeter of the otherwise square shaded area.
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Nice answer, perfectly explained so I have nothing further to add on the solution.
My older brother has a Maths O-level from 1975, grade C I think and has no higher level education apart from being a qualified electrician. He is very practical at problem solving and managed to get an outline answer in his head. He correctly worked out the side of the square and the area of the four extra points, estimating the result as 13 to 14 (assuming a=1). Pretty impressive!
Mrs R found the teaser from the Express newspaper (on-line). In contrast their solution (with two errors!) was:
A square is 3 x 3 = 9. The area of a triangle is (a+b)/2 = (1+1)/2 = 1.
As a result, the area of four triangles = 1 x 4 = 4 and the area of the star is 9 + 4 = 13.
I don’t think it was unfairly hard for GCSE. The hardest questions are meant to distinguish between A* and A**, so should be too hard for about 90% of candidates.
Ooopps,
In the section headed ‘TOTAL SHADED AREA’, the second line, starting 4a^2 + 2…
There is only one ’ + 2a^2’ at the right-hand-end. There should be another ’ + 2a^2’.
Don’t now how I missed it off, possibly when I scanned and cropped the original ?
Anyhow, the third line clearly picked it up to produce the ‘8a^2’ term at the start of the line.
Apologies.
When Mrs R marks her students’ scripts, she would knock off just half a mark for typos and other intermediate slips. Since she then rounds up to a whole mark, single slips are not penalised.
I hadn’t spotted it, but if it starts and ends right then I don’t check every line.
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Finding a pair of socks in the dark !
I have 20 pairs of socks. Each pair is different to each of the other pairs. They are randomly shuffled up in my sock draw as loose socks rather than folded together as pairs.
On a dark early morning last winter, I picked a sock at random. I then picked another sock at random from the remaining socks.
What was the probability that the two socks made a pair ?
Chicken is a small gold mine town. Back in the day, the un-named town had to come up with a name. The resident population, mainly miners, agreed to call it Ptarmigan after the delicious local birds that they were eating.
However, they couldn’t agree how Ptarmigan was spelt, so settled instead on Chicken.
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It’s less than the probability of discovering too late that they don’t match and being self conscious about it all day at work.
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I’m pretty good with the easy ones–There are forty socks in the drawer to start with. You remove one, leaving 39. One sock in the drawer matches the sock that you took out, so there is one chance in 39 of pulling a matching sock on the first try.
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Spot-on JR. And very nicely explained.
I also like the fairly easy or straight forward ones. And it’s still very satisfying when you solve them.
Hope you enjoyed it.
A Special Box of Chocolates !
Last weekend I bought Mrs D a special box of chocolates. Unfortunately, all the chocolates were identically wrapped.
However, the chart included in the box assured us that the box contained 8 caramels, 6 truffles and 4 pralines. It also informed us that half of each type of chocolate were coated in dark chocolate and half were coated in white chocolate. Mrs D doesn’t like pralines or white chocolate, but she does like all the others.
She selected her first chocolate at random (well, they were all identically wrapped !!)
A) What was the chance that she selected a white-coated praline ?
B) What was the chance that she selected a chocolate that she likes ?
PS. why not buy a box of chocs to enjoy whilst figuring this one out 
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