By the time I added the gin I forgot the question!
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Let’s assume that the second larger glass is 1,000ml.
So the first glass is 500ml, of which there is 250ml orange and 250ml lemon.
The second glass is 1,000ml, of which 200ml is orange and 800ml is lemon.
So the jug is 450ml orange 1,050ml lemon, total of 1500ml. So, 30% orange and 70% lemon. This will be very sour and won’t be saved by any quantity of gin 
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Mrs R’s answer: “0.5 for the first, two-fifths for the second gives 0.9 orange in 3 glasses worth. Gosh, it’s a bit lemony!”
1st son: “Yeah 30%”
2nd son: “Yeah 100%”
I think Mike’s solution is somewhat better explained than my lot!
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Not exactly a ‘Brain Teaser’, but I found it mildly interesting …
… I was trying to help my 15 year old grandson with a bit of extra practise with his maths. He was revising equations of a circle and straight lines, all based on cartesian co-ordinates.
I asked him to plot the following two equations and then tell me the co-ordinates of their intersection(s). I had intended to give him a circle centred on the origin (0,0) plus a diagonal straight line passing through the origin, at 45 degrees to X/Y axis, sloping down from top left to bottom right !
For the circle, I gave him a^2 + b^2 = 25
But I made a mistake with the equation for the straight line.
Instead of y = -x
I gave him y = 1 - x
To my surprise, the co-ordinates of the intersections were quite neat numbers, rather than the relatively messy numbers he would have got with y = -x
Give it a try, see what you think !
It took me a few minutes to envisage it. A Pythagorean triple?
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Not sure if I have understood this correctly, but by some elementary trial and error I got y = -3, and x = 4 for the “neat numbers”, and y = -3.535534 and x = 3.535534 for the “messy” ones.
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Hi Steve, Hi Ravvie,
I have up-loaded my diagram.
It shows the circle, centre (0,0) Radius 5
And the straight line y = 1 - x
The straight line forms a chord passing through (0,1) and (1,0)
The length of the chord is sqrt(98) ie just a bit less than the diameter which is 10.
The chord intersects the circle at (-3,4) and (4,-3)
That is what I thought was ‘mildly interesting’, especially since it came about by mistake when I wrote y = 1 - x for the straight line rather than y = -x
And yes, I also felt that sqrt(12.5) [ie 3.5355] was messy !
A pint of Water ?
Mrs D is baking and needs a pint of water. She only has a 3-pint jug and a 5-pint jug. Using only these jugs and water from our tap, how can she measure exactly one pint of water ?
Full the 3 pint jug twice pour into the 5 pint jug and whats left is the pint.
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Well done Pete, and nice description.
Enjoy the virtual champagne and cigar 
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This is like the old, “what’s heavier, a pound of feathers or a pound of lead?”.
She is right, by the way but has created more work unnecessarily. Familiar territory😂
Yes, she is right. Any imbalance on one side is off-set by the same amount if the same weight is used again on the opposite side of the scale.
Hi guys,
I tried the arithmetic, using scales with lever arms 9 units and 10 units (eg inches since that gave me a better “feel” as to what was happening !)
After a couple more arithmetic examples (4 units and 5 units) I gave it a shot with algebra.
I came to a different conclusion to your goodselves
PS, from a practical point of view, there wasn’t a lot in it. The differences were quite small.
Here is one of the sample solutions that I mentioned, using an off-set scale, 4 units v 5 units, and aiming to weigh out 4 lbs of flour.
Mrs D’s comment was along the lines … “it’s close enough, unless YOU want to take over all the cooking !!”
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That will be one huge cake!
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When I explained to her that with one balance-arm slightly longer than the other she will ALWAYs be measuring MORE than required (using her current technique as above), she asked whether she would ALWAYS be measuring LESS than required if one balance-arm was slightly SHORTER than the other …
… I gave up !!
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You could suggest that Mrs D makes two cakes, using the two different methods. Then put the cakes on the balance to prove that they weigh the same.
Two big cakes, what’s not to like?
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USA - Canada Border
How long is the border between the USA and Canada ?
Answers in Statute Miles (preferably) but km will also do
PS. At least have a guess before you Google it !!!