The block
He's in two minds on the matter. (The block, of course, like everything else, is made of matter).
How old?
Melissa is thirty. Take the vowels in their names, and assign the values a=5, e=10, i=15, o=20 and u=25. Then add up the vowel values for each name. (Allen is fifteen, being nearly sixteen.)
Two iron bars
Touch the end of one (call it A) to the centre of the other (call it B). If there is a strong attraction, then A is the bar magnet. If there is negligible attraction, then B is the magnet.
More matches
There are two alternative solutions:
(Roman) 5 = (binary) 5 (Head up=1, head down=0, or vice versa)
Root 1 = 1
Pentominoes
1: The pentominoes are placed in the order V, Z, Y, W, T, F, S, L, I, P, X, U, as shown below:
2: The pentominoes are placed in the order V, L, S, F, T, W, Y, Z, I, P, X, U, as shown below:
Each of the above solutions can be turned over to give an (arguably) alternative solution.
Two balls in space
The two spheres are weightless, but they still have mass and so inertia. Try pushing one hand against each of them at the same time, and the difference will be obvious. The solid one will offer more resistance than the hollow one.
Three utilities
If one considers this as a problem in the plane, i.e. in two dimensions, then there is no solution. However, from a purely utilitarian point of view it can be done. Most of the pipes or cables can be laid without problems; it is only the final two that present difficulty. The two companies laying these two simply run them side by side to the nearest spot where there is a cave in a cliff face or something similar. Then they diverge. One goes up, and across the cliff top. The other goes down to the cave mouth, and runs in through it, and then up through the cliff to come near to the surface the other side of the first cable. Then they run them back to the houses. Of course, it could be an expensive exercise if the nearest cave is miles away, but it does solve the problem.
The extra square
There is no extra square. The "diagonal" of the rectangle is in fact not a straight line, but only appears to be so because the angles of the edges along it are so similar. There is actually a long thin gap in the shape of a parallelogram between these edges, and the area of the parallelogram is exactly one square unit. So the area enclosed by the edges of the rectangle is 34x13=442, but the area of the pieces is 442 less the area of the gap. The three measurements in the diagram are three consecutive Fibonacci numbers. This puzzle works with any three consecutive Fibonacci numbers, but as the numbers chosen move up through the series there is alternately a gap then an overlap of pieces in the rectangle.
"Now, I know..."
It is a mnemonic for the first 9 digits of pi. The numbers of letters in each word represent the digits, and the comma the decimal point.
What am I?
I've known this for many years, but never known an answer to it. If you have the solution, please let me know. If I receive a satisfactory solution, I'll enter it here. To date, I've received two suggestions. Two people have suggested a mirror, and another has suggested a lie. Both are good, but I'm still not convinced there isn't another answer.
Update, 27 Feb 2001 Two emails on two consecutive days, each suggesting "nothing". Another good answer - I suspect there may be more that fit too, and I haven't thought of any myself!
Update, 27 June 2001 An email suggesting the answer is a paradox. Now that, I think, is an excellent answer.
Update, 10 Aug 2001 Another email suggestion - a shadow. There seem to be a lot of possibilities.
Update, 5th February 2003 Alan Wright has pointed out that "je suis" means not only "I am" but also "I follow", and sent the following, which I think is probably the intended answer:
Je suis que je suis
Mais je ne suis pas que je suis
Parce que je suis que je suis
Je serais un âne.
I am what I am
But I am not what I follow
Because if I follow what I am
I would be an ass.
A little light verse
Spoken aloud, it is (almost) the following nursery rhyme:
Sing a song of sixpence,
Pockets full of rye,
Four and twenty blackbirds
Baked in a pie.
One hundred
The solution given most often is:
1 + 2 + 3 + 4 + 5 + 6 + 7 + (8 × 9) = 100
Possibly the one using the fewest signs (and no brackets) is:
123 - 45 - 67 + 89 = 100
Some others are:
(1 × 2 × (3 + 4) × 5) + 6 + 7 + 8 + 9 = 100
- (1 × 2) + 3 + 4 + (5 × 6) + (7 × 8) + 9 = 100
(((1 ÷ 2) + 3) × 4 × 5) + 6 + 7 + 8 + 9 = 100
((1 + 2) × 3 × 4) + 5 + (6 × 7) + 8 + 9 = 100
- (1 + (2 × (3 + 4 + 5))) + 6 + (7 × (8 + 9)) = 100
Still more matches
The bottom left match is placed across the top to give a "9".
Matches
Date change
Always. Octal 31 always equals Decimal 25.
Odd ones out
1: 57. The others are prime numbers.
2: Rats. The others are languages. (Sorry, that is rather obscure!)
3: Static. The others are anagrams of composers' names: Elgar, Verdi, Chopin, and Haydn.
Knights and Knaves 2
B claims that A said he (A) is a knave. No knight would lie and say that he's a knave, and a knave would not tell the truth and say it. Therefore A did not say that, and so B is a liar and thus a knave.
C said that B was lying, and indeed he was. Therefore C is a truthtelling knight.
It cannot be determined which A is. We don't know what A actually said. He may have said that he's a knight, but he would say that whichever he was. Or he may not even have answered the question; he might have said something like, "Sorry, what did you say?"
Something entirely different
There is, as I said, no "set solution". These are merely a few thoughts that occur.The sun and the moon would, of course, rise in the west and set in the east. The day would be a little shorter, but there would be more days in a year. Perhaps our measurement of time and our calendars would be entirely different as a result. Weather patterns would be different, as the Coriolis effect would be reversed and so the movement of air masses would be altered.
I'm sure there's much more - I would be interested to hear any comments on this. Feel free to contact me.
Update, 28 October 2001: I've had an email suggesting that toilets, shower drains, sinks, etc. would drain in the opposite direction. I don't know whether it's true that water draining from sinks and so on does indeed swirl clockwise in the Northern hemisphere and anti-clockwise in the Southern, but if that's so then the direction would indeed be different in this scenario.
Knights and Knaves 1
There are many possible solutions. One would be to ask: "If I were to ask you whether you are a knight, what would you answer?" If you did ask an inhabitant if he were a knight, he would answer yes (a knight truthfully, and a knave falsely). Thus if you ask the above question, the true answer can only be yes. So a knight will say yes to that question, and a knave will say no. In fact, each answers exactly as if they were truthfully answering the question "Are you a knight?"But there is a much simpler type of solution. In Werner Herzog's film The Strange Enigma of Kaspar Hauser, Kaspar is being interrogated with a view to establishing his powers of reason. He is given this problem, and infuriates his questioners by replying that he would ask the inhabitant, "Are you a tree-frog?" Here the knight will of course answer no, and the knave yes.
And that is all that is needed. Any question with a self-evident truth as answer will show whether the inhabitant is a knight or a knave.
The portrait
He is looking at a picture of his son.
He says, "This man's father is my father's son." His father's son can only be him or a brother of his, and as he has no brothers, it can only be him. So what he says is equivalent to, "This man's father is me." Or, if you like, "I am this man's father." Thus the portrait is of his son.
Black King
1: He would be stalemated at h1.
2: He would be checkmated at e3.
3: He would be checkmated next move at a8. (Qc8 mate).
4: He can never be checkmated at h1. (Because he is already stalemated).
An enantiomorph is a "mirror image" which is essentially different from the original. Take letters of the alphabet as an example. Draw capital letters in a sans serif font which has all strokes of equal thickness. Cut them out. Place letter T on a flat surface and draw around it. Then lift it up, flip it over and place it down again. It will of course fit the drawn outline. Likewise letters A, O, V, etc. Some letters may need to be rotated after flipping them over, but will then fit. But do the same thing with letter F, for example, and when you flip it over and replace it, it can not be made to fit into the original outline, no matter how it is rotated. The "two" letter F's are enantiomorphs. In three dimensions, an obvious example of enantiomorphs is a pair of gloves.
The series of Fibonacci numbers begins: 1 1 2 3 5 8 13 21 34 55 ... The sequence is formed by adding the last two terms to get the next. It is named after Leonardo of Pisa, known as Fibonacci or son of Bonacci.
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© Bill Daly 2000 - 2007