Just to tidy up the Singapore - Equatorial Guinea teaser …
… the 10,000 km from Singapore to Equatorial Guinea followed by the 10,000 km North, puts the aircraft over the North Pole. The distance from the Equator to the Pole is 10,000 km (as defined by France in c.1793 thus establishing the length of one metre)
There is only one direction to travel when departing the North Pole → … South 
Just point the aircraft towards Singapore and 10 hours/10,000 km later you’re home !
Hah, so the earth isn’t flat after all.
“Impossible” GCSE Maths Question
If anyone thought exams were getting easier, try this one which caused a stir recently amongst GCSE students. It is hard, but not impossible.
Well, I’m glad I’m not doing my O Levels this week.
A quick shot suggests 16(√2 – π/3)
5.87 cm² 2dp
But I haven’t checked it so I’ll take a closer look this evening … there’s an awful lot of 2’s and 4’s and 16’s plus writing “shape” “segment” " sector". Very easy to get muddled.
Just seen a couple of errors in my arithmetic (eg that sqrt 2 should be a sqrt 3) and also spotted a more straightforward solution.
Because if Box No 8 did NOT need repairing he would have said 5 of the first 7.
My handwriting isn’t great, but I thought a scan of my 1st attempt might prompt others, especially if I have made a gross blunder !!
I did check it with a slightly different approach, but this wouldn’t reveal any gross blunder, it relies on the same logic !
Perfect answer, Don.
As with many a problem, maths or otherwise, it helps to break it down into easier sub-problems. In this teaser, breaking the shape down into a combination of simpler ones: an equilateral triangle and a circle segment. These are straightforward to measure their areas.
One other piece of information was a useful hint. Namely to show the answer in terms of π. Circles, areas and π is a big hint that πr^2 will feature and a circle segment fits the bill.
Thanks Ravvie for that “teaser”. I agree with the general view that it was a difficult question for a GCSE paper.
I found it took a lot of concentration to keep track of the segments and triangles - as a result, I used a couple of variations to check my initial answer.
In addition of course, you needed Pythag (or some other means to work out the area of the equilateral triangles (sqrt 12 is 2xrt3, not 2xrt2 !) and to confirm that the angles are indeed 60 deg - hence Cos 1/2.
Quite a challenge for a 16 year old under exam pressure.
Spot-on Explorer. Well done !
O Happy days !!!
We enjoyed a terrific family birthday celebration last weekend in a large hotel down in Cornwall.
We hired a small hall on the ground floor for the dinner and enjoyed a range of party games afterwards before retiring for the night in our rooms on the fifth floor overlooking the sea.
When we got into the lift (elevator for our American cousins), I had a bowl of water on the floor with an apple floating in it, (left over from the bobbing apple competition), hovering beside me was a helium filled balloon that was perfectly balanced, neither floating up nor down. We also had, suspended from the ceiling of the lift, a bag of sand (don’t ask !) attached by a large rubber band.
When the lift accelerated upwards, I noticed that ……. Oh, you tell me !
Did the apple sink or rise in the water ? or what ?
What did the helium balloon do ?
What happened to the bag of sand ?
The apple sunk in the water, the ballon stayed in the same relative position between the floor and roof, and the bag of sand moved towards the floor as the lift went up and then rebounded towards the roof when the lift stopped and then jiggled up and down until it returned to the original relative height from the floor.
There isn’t enough information to establish whether the sand bag hits the apple and spills the water out, or hits and disturbs the ballon.
Two out of three is very good Mike.
The sand bag doesn’t disturb either the apple or the balloon. It was quite a large lift. Plenty of room
I had the same as Mike, so I don’t know which two are correct.
I was less sure about the balloon. When I learned physics over 40 years ago I don’t think that objects in an accelerating fluid (air) was part of the syllabus.
Hi Mike, Hi Ravvie,
You both got the balloon and the sandbag correct.
The apple in the bowl of water is the same as the balloon in a lift full of air. Relative to the water, the apple remains stationary.
Mind you, I recall this teaser from many years ago. I know the answers are those given at the time. However, I have never got around to carrying out any actual experiments myself (despite the wording of the teaser ) I think the apple in a bowl of water would be the easiest to accomplish
I am surprised about the apple. Based on Archimedes Principle (before lifts were invented!) an object displaces its own weight of water. If the upward acceleration is a constant 0.1g for example, the apple will be 10% heavier, so should sit 10% lower in the water.
Mrs R (who has a 1st in Physics amongst many other qualifications) instinctively thought that the balloon would go down as the “air will become thinner at the top of the lift”. I think she may have a point, though this is not my strong point.
I think the water will also be 10% heavier …
There will no doubt be nuances regarding all three activities, eg when the lift is accelerating : running at a steady speed : decelerating. The steady speed situation is probably the one around which the basic answers were provided.
As for air density inside the lift, I guess we could assume the lift is more or less airtight whilst the doors are closed. But yes, air density reduces with altitude, as does pressure and generally so does temperature.
As I say, lots of nuances
Can you identify a natural number, whose letters appear in alphabetical order when spelt out ?
Best if we limit this to standard English !
Forty?
