What number should replace the question mark ?
72
Nicely done Eoink.
Different people think of it in different ways.
Multiply the top two numbers and add 50%
That’s how I got there. I spotted that the products of the top pair needed to be multiplied by 1.5 to reach the bottom.
For the benefit of anybody who has tried the “how many rectangles” teaser, the answer is 23.
Point of No Return .
The Point of No Return (PNR) or Point of Safe Return as it is now referred to. ………
…………is the furthest point along a planned route to which an aircraft can fly and return to the departure airfield or departure alternate, within the Safe Endurance of the aircraft. The Safe Endurance is the amount of time that an aircraft can fly without consuming any of the mandatory reserves of fuel it is required to have overhead its departure airfield or departure alternate in the event of the aircraft returning from the PNR.
Phew, that was quite a mouthful. It means we need only consider the amount of fuel to go from an airfield, to the PNR and back to the airfield (ignoring the possibility of using the departure alternate for simplicity).
As a further simplification, we shall assume that the aircraft flies at a constant, steady true airspeed and that likewise, the wind remains constant throughout.
D = Distance to the PNR (from the departure airfield)
E = the Safe Endurance
A = the True Airspeed of the aircraft
V = Wind Speed (headwind one way, tailwind the other way)
All I am looking for is a formula for D
And, just to ensure the formula works, assume :-
E = 10 hr
A = 300 kts
V = 50 kts
If you can’t derive a formula, but can “juggle” the figures, a value for D will do, ideally in Nautical Miles (well, the speeds above are in knots !)
The attached slide sets out the fundamentals.
Ignore the time taken to turn at the PNR (it would be one minute normally). Groundspeed is simply True Airspeed (A) +/- Windspeed (V)
This is the basic formula.
It allows for variations in outbound/inbound wind and airspeed.
Of course it can be simplified further if (as in the problem set) the airspeed and windspeed are constant throughout.
So, assuming a safe endurance 10hr, a constant true airspeed 300kts throughout and a steady headwind 30kts outbound, 30kts tailwind homebound (ie a constant wind throughout …
The outbound time to PNR is ??
The distance to PNR is ??
Substituting in the two formulae above
E = 10 hrs
O = 300 + 30 = 330 kts (assuming tailwind outbound)
H = 300 - 30 = 270 kts
Hence T = (10x270)/(330+270) = 4hr :30mins
And D = (10x330x270)/(330+270) = 1485 nm
I have used the 30kt windspeed mentioned above, and appreciate that I quoted a 50 kts windspeed in the original post. Try using the 50kts wind speed. Then try using the 30kt windspeed in the opposite direction to that used in this post. the time to the PNR changes, but what about the distance ?
Two big bags, non transparent. 50 red sockets in one. 50 black sockets in the second bag.
Your eyes are closed and you pull out one socket per try.
How many tries do you have to do to be sure to have a pair ?
PS: one try = 1 socket chosen.
you can choose only one bag or both.
Hi FR, thanks for posting a Brain Teaser. Can you clarify the following …
By “a pair” do you mean
- one red plus one black, or
- two sockets of the same colour or
- just any two sockets ?
When you say “you can choose only one bag or both” this implies that you know which bag is which, even if you don’t know which bag contains red sockets and which bag contains black sockets. Is this correct ?
In french, a pair are two sockets of the same color. So 2 red or 2 black only possibilities.
Not the same term in English?
Yes, you don’t know which bag contains red or black. The two bags are in front of you and you can choose any bag you want, without seeing and without knowing which bag has the red or black.
Only one socket per try.
No, not the same term in English. A “pair” simply means “two”
Any of my three options above could be classified as a “pair”
If you asked a retailer for a “pair” of speaker sockets (for example) he might well assume that you wanted a red one and a black one.
But when you buy sockets, they are in general in same color and two.
So how you name the combo?
3 tries I suppose, assuming that the pairs don’t need to be consecutive, i.e. if I went black, red, black I could call the two blacks a pair.
The real question, sorry to say it late, but ordinary I speak French : how many MINIMUM tries do you have to do to be SURE to have a pair ( 2 of same color) ?
I am waiting Don to give the answer.
Ok.
So the first try delivers either red or black. Let’s say red.
The second try could deliver either red or black. If it’s red then bingo you got a pair in two trys (this is the minimum, but not guaranteed)
The third try if needed, (ie you have one red and one black) will deliver either a red or black, but either way, it will match one or other of the sockets that you already have selected.
So, the minimum number of trys to guarantee “two sockets of the same colour” is three.
Not necessarily.