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    I remember this one: the answer is the number of letters in the word!


    1) The probability is 0, because if 3 letters are matched correctly then so is the remaining one
    2) The three points lie on a unique plane if they don’t form a straight line. The only way they would form a straight line is if the centre of mass is on an edge, which isn’t the case for a tetrahedron of uniform mass.
    3) I can think of three ways, but all of them involve something more than a thermometer.
    4) There are no more examples. Every three consecutive odd numbers contains a multiple of 3. Three even numbers are obviously not all prime.
    5) Why should it not be able to return to its starting point? Do you mean that it gets too tired after walking 4 kilometers?
    6) What if you take three pills? Is that dangerous?


    They shut of the light?


    1: Zero

    2: Any three points in 3D space lie on a single plane. If a third vertex lay on this plane then the fourth point must also be in the same plane for its centre of mass to be on that plane (otherwise there would be a component of mass in a direction perpendicular to the plane), making it completely flat. A flat tetrahedron would have no centre of mass as it would have no mass, so this cannot be the case. As a result only the two vertices we chose can line on the plane.

    5: Yes: start half a km away the North Pole. This way the movements east and west both occur on the same line of latitude and so cancel each other out. Of course, this assumes that you keep the same direction when crossing the Pole even though your north and south would flip.

    6: Consume all four pills


    Hi all,
    Some nice responses to my questions, well done! To clarify a few matters:

    There are a few assumptions for this problem:
    1. The Earth can be assumed to be a perfect sphere of radius ≈6400km (the exact value is not important).
    2. West/East are along the lines of latitude.
    3. North/South are along the lines of longitude.
    4. The Arctic Circle is defined to be the area of the Earth more than 66°33’ North.

    Because of this, there probably exist solutions where the starting point is within 1km of the North Pole, but the ideal solution(s) exist where the bear starts more than 1km from the North Pole (so it never crosses the pole). Have fun!

    You must consume exactly one red pill and exactly one blue pill (to within about a quarter of a pill each). Taking more pills than this is an overdose and will kill you…


    For those wanting to get started on my Q3, I present one solution here: Drop the thermometer from the top of the building, and time how long it takes to crash on the ground. Call this length of time t. Then the height of the building is given by gt²/2 where g is the acceleration due to gravity (≈9.81m/s²).


    6) Are the pills of a type that can be broken in half? In which case, swallow a half of each pill.


    For question 6:

    I would take half of each pill, thus guaranteeing that I take one of each coloured pill.


    Emelia’s Father has 4 children – Elizabeth the 1st, ELizabeth the 2nd, Elizabeth the 3rd and one more child.

    Suggest a possible name for the 4th child.


    Here is a new one, a true story that happened hundreds of years ago.
    The secret to saving oneself from poison was to drink a stronger poison.
    There was an excellent physician who served in egypt’s elite circles, who was asked to compete against a rival. They each had to create a poison and drink first the opponent’s, then their own. Our physician created a ‘poison’ made of diluted wine. He drank the other’s, then his own and survived. The opponent did the same and died. How come?





    The physician drank a weak poison before the competition.

    The reason why this works is that, as mentioned, a stronger poison acts as a cure for the weaker poison, neither having an effect. So, when the competition started, the physician drank the opponent’s, undoubtedly strong, poison, which countered the poison already in his system, and then he drank harmless wine.

    The opponent, on the other hand, had no poison in his system prior, so the drink of wine did nothing, and then he drank his own poison and died.

    I’ve heard this one before, but in a slightly different context (I’m pretty certain there was a king involved somewhere).


    I suggest: Hidee the 1st – (do you get it?)

    Anyway no need to suggest a name when her name is already given!
    Her name is obviously Emelia, she being one of the four children her Father has.


    Using my thermometer (Wilko fridge/freezer thermometer) I used two methods to estimate the height of my local Morrisons. One method gave 6.4 metres, but the other method gave 5.7 metres. Neither of these methods involved accessing the roof of the building!


    Sorry, not Emilia but Emelia.

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