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    – Holding the thermometer at a position that the top of the building lines up with 40 degrees and the bottom of it with -40 degrees, a sign on the wall takes up about 10 degrees, so its height is about an eighth of that of the building. The sign is 80cm tall, so the building is 6.4m.
    – Tape the thermometer to the window with a view to the building. Stand in a position that the top of the thermometer lines up with the roof and the bottom with the base. While standing in the same place, hold a glue stick so that it lines up with the thermometer and the building. (My arms aren’t long enough for this, so I set up slats from old blinds and taped the glue to it, then adjusted it until I could stand in a position where all three line up.) Measure the glue stick, the thermometer and the horizontal distance between the two. Use a map to find the distance between the two buildings, then draw a diagram of all this and use trigonometry to calculate the height. This method gave me a height of 8.8m for the same building. It’s hard to be accurate because a small difference in the height of the glue stick makes a big difference.
    – Here’s a method I haven’t tried: Using the thermometer as a weight, tie it to the end of a long string and lower it from the roof.
    9) It’s possible that a different player remembered and told her.
    12) Start 1+1/(2pi) from the south pole.


    Nice. I had that as one of my solutions (but with an approximation of 1°C every 100m).

    Q3: Nice methods!
    Q9: True, but… what if no-one remembered? (Perhaps a bright light caught everyone’s attention instead…!)
    Q12: Correct! (Well – more or less. The exact distance from the South Pole is actually [1km + (R * arcsin(1km/2πR) / 1rad)], where R is the radius of the Earth, but I think that (1 + 1/2π)km is close enough.)


    Why choose gods for the puzzle?!


    7) seven days
    8) it’s a bungalow, there aren’t any stairs!
    9) She was interrupted on one of the first four cards, right?
    12) No?
    The rest of them) I have absolutely no idea!


    A puzzle related to @The_Letter_Wriggler post #91790 in the Maths forum. It is taken from ‘Puzzles and Curious Problems’ by Henry Dudeney.

    221. – THE FLY’S JOURNEY

    A fly, starting from point A, can crawl round the four sides of the base of a cubical block in four minutes. Can you say how long it will take it to crawl from A to the opposite upper corner B?

    The question is accompanied by a diagram where A and B are diametrically opposite points on the cube.


    I have a hypothesis and even better a hypotenuse.


    Notes on my questions: A lot of my questions are taken from the book ‘Mathematical Magic Show’ by Martin Gardner – a good read! All other problems are taken from either other (well-known?) sources or my imagination. (I have more coming up…)


    Q8 is correct!
    For Q9… what if she was interrupted after the first four cards?


    I provide three different solutions:
    1. If the fly can only travel along the edges, 3 minutes.
    2. If the fly can travel through 3D space, sqrt(3) minutes.
    3. If the fly can only travel along the faces, sqrt(5) minutes.


    Q3 had me thinking about how more solutions might exist in the future that aren’t possible now. Here’s a different riddle, where it’s clear that things have changed:
    How many ways can you think of to do shopping using a phone, if the phone is:
    a) a corded landline with no extra features ☎
    b) a mobile phone with text, calculator etc. but no internet/data/browser and no way to install applications that didn’t come built in
    c) a smartphone 📱
    There are at least three solutions for part a.


    It does not fly so it crawls along the hypotenuse of a triangle whose sides measure 2 and 1 units.
    It takes it sqr(5) mn.


    Hi all,

    To clarify matters on Q9, I have provided a more specific version that links more directly to the solution I had in mind. Hope this helps!

    9) (v2) 52 cards are meant to be distributed to A,B,C,D,A,… as described above. However, this series of deals stops after n cards, and no-one knows the value if n. You need to come up with an algorithm of the form “For all x in [fixed list of people in {A,B,C,D}], deal one card to x until all cards have been dealt”, such that everyone ends up with 13 cards by the end and it is independent of n.

    For instance, a sample list could be [A,C,D,B,A,C,D,B,A,…]. In this case, if 3 cards have not been dealt, they go to A,C,D in turn. If 5 cards have not been dealt, they go to A,C,B,D,A in turn, and so on. (Obviously this list is not the answer!)


    TRICK PUZZLES (and some not-trick ones) – PART 3
    (I am now running seriously thin on novel ideas…)

    First, I present some (more) mathematical puzzles:

    13) In a magic trick, a magician takes a standard set of double-six dominoes and removes the doubles. He asks a member of the audience to remove one domino (ideally at random), and arrange the other 20 to form a chain, all without the magician watching. The magician now looks at the chain, and instantly identifies the domino that was removed.

    How does the trick work? And why does the magician insist that the doubles are removed first?

    14) (Based on #89246) A book is opened to some arbitrary page. Unfortunately, some of the pages in the middle have been removed, so the two page numbers are not consecutive. Is it possible that the page numbers of the two shown are n and n² for some integer n?

    15) The following ‘proof’ claims that 1=2, which is obviously wrong. Find the error.

    Let x be a number satisfying x-1=2x-2. Then:
    1/(x-1) = 2/(2(x-1)) = 2/(2x-2) = 2/(x-1)
    Multiplying by (x-1) yields 1=2, as desired.

    16) Let ABCD be a rectangle. Let M,N,P,Q be the midpoints of sides AB,BC,CD,DA respectively. Show that lines AC,BD,MP,NQ concur – that is, show that they meet at a single point. (Challenge: Show that this remains true even if ABCD is a parallelogram.)

    Now some crosswords!

    17) This crossword contains six words but only two clues… Gold luck!

    (Here ? means a white square to be filled in; _ means a black square to NOT be filled in.)

    Messages. (5)
    Bowl with holes? (5)

    18) All clues fit into a 3×3 grid with no gaps.

    Clues (Across):
    1. (e.g.) Black or green.
    2. Anagram of Greek letter.
    3. Past tense verb.

    Clues (Down):
    1. Anagram of 3 Down.
    2. What you might do at lunchtime.
    3. Sounds like number.

    19) All clues fit into a 4×4 grid with no gaps.

    Clues (Across):
    1. ROT-13 cipher applied to 2 Across.
    2. Can be made from the letters in BANANA.
    3. Girl’s name.
    4. Anagram of 3 Across.

    Clues (Down):
    1. Word with double letter.
    2. Name of two of Henry VIII’s wives, with one letter changed.
    3. Palindrome.
    4. Bread.

    The final puzzle here is definitely not a trick puzzle, but I have put it here because of how interesting it is. Enjoy!

    20) After engaging in some dodgy actions (we will not disclose them here…!), you have been forced into playing a game with the Devil.

    Here is how it works. The Devil writes on a blackboard the numbers 1 through 100. Beginning with the Devil, each player in turn colours one of the 100 numbers red, as long as it was previously uncoloured and it is either a factor or a multiple of the previous number to be coloured (if one exists). The first player that is unable to make a move wins.

    For instance, a sample game could go:
    41 → 82 → 1 → 86 → 2 → 94 → 47
    And now the second player wins, since they are unable to make a move (both 1 and 94 have already been coloured).

    Now, it is not too hard to see that the Devil will (comfortably) win with best play. (Challenge: Prove this.) However, in an act of religious miracle, a heavenly angel comes in and orders the Devil to begin with the number 13, giving you an advantage.

    Can you now beat the Devil? If so, how do you respond?


    Re. #92221:
    Did I put ‘Gold luck’ in Q17? (Oops!) I meant to say ‘Good luck’!


    I provide a couple of different solutions for (a). I assume here that you have arranged, or will arrange, some way of transferring any payments at a later stage.

    1. You could just telephone the supermarket and tell them what you want to order. (This is a boring solution.)

    2. You could also have some form of system where after calling the supermarket, you press the extension button (#). Pressing certain buttons will then correspond to certain products or certain actions (e.g. 00=milk, 01=cheese, 99=cancel last product, etc.). If you think this solution is far-fetched, someone actually used Teletext/Videotex to do shopping from home! (The story is at, for example,

    3. Get someone else to do the shopping for you. In return, offer them the corded landline.


    Some good answers. This question is in the same spirit as yours about measuring a building with a thermometer, so as long as at least some part of the phone helps in some way with shopping then that’s a valid answer. So answers for (a) could also begin “Unplug the landline, take it to the shop…” or “unplug the landline, fetch a screwdriver…” etc.


    @TLW, your last pyramid has two solutions. Three if 0 is allowed.


    @madness and every one else: So Sorry they were not the ones I intended, I gave the wrong list to Harry, hoping he will put the new list up soon
    Best TLW.

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