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Crosswords and other puzzles
For discussion of all forms of mental gymnastics, especially that baffling final clue
Message board > Crosswords and other puzzles | 71 to 120 of 153 |
by Richard - Wed 28th Dec 2005, 11:52pm | ||
Richard said: The Royal Parks Website suggests that there are only 8 Royal Parks. The quote from the site is;Millions of Londoners and tourists visit the eight Royal Parks for free each year. | ||
by Richard - Wed 28th Dec 2005, 11:51pm | ||
gf said: Depending on which one you believe from a selection of four sources I've found so far, there are 8, 9, 17 or... 10 Royal Parks. The Royal Parks Website suggests that there are only 8 Royal Parks. I'd say that would be a fairly reliable source | ||
by gf - Wed 28th Dec 2005, 12:03pm | ||
Depending on which one you believe from a selection of four sources I've found so far, there are 8, 9, 17 or... 10 Royal Parks. | ||
by gf - Wed 28th Dec 2005, 10:43am | ||
Is it possible that this quiz has been set by somebody non-sporty who thinks there are 18 Teams In The Premiership? | ||
by gf - Wed 28th Dec 2005, 10:33am | ||
mjb said: 3 Coins In A Fountain 12 Good Men And True | ||
by mjb - Tue 27th Dec 2005, 11:13pm | ||
3 CIAF 3 Coins In A Fountain | ||
by Richard - Tue 27th Dec 2005, 10:44pm | ||
4 PIAPT 4 Players In A Polo? Team | ||
by mjb - Tue 27th Dec 2005, 10:28pm | ||
10 DS 10 Downing Street | ||
by Richard - Tue 27th Dec 2005, 10:16pm | ||
22 TLD 22 - Two Little Ducks | ||
by mjb - Tue 27th Dec 2005, 9:26pm | ||
jmg said: 2 Swallows Don't Make A Summer2 SDMAS 36 BKOAP 6 BIAO 7 DS 36 Black Keys On A Piano 6 Balls In An Over 7 Deadly Sins So it's just these ones left : 18 TITP 30 MSIABUA 12 GMAT 4 PIAPT 10 DS 3 CIAF 22 TLD 10 RP | ||
by mjb - Tue 27th Dec 2005, 9:17pm | ||
jmg said: ... questions like "12 DOC" to which the answer is "Days of Christmas" ... 4 Calling Birds ?4 CB | ||
by jmg - Tue 27th Dec 2005, 6:39pm | ||
jmg said:200 PFPG Just got this one... pounds for passing go | ||
by Richard - Tue 27th Dec 2005, 6:37pm | ||
10 GB (HOTW) 10 Green Bottles (Hanging On The Wall) | ||
by Richard - Tue 27th Dec 2005, 6:33pm | ||
3 MFASBE 3 Minutes For A Soft Boiled Egg?2 WDMAR 2 Wrongs Don't Make A Right? | ||
by Richard - Tue 27th Dec 2005, 6:23pm | ||
26 LOTA 26 Letters Of The Alphabet | ||
by jpd - Tue 27th Dec 2005, 5:42pm | ||
9 LOAC 9 Lives of a Cat | ||
by jpd - Tue 27th Dec 2005, 5:39pm | ||
5 OR 5 Olympic Rings3 FIOY 3 Feet in One Yard | ||
by jmg - Tue 27th Dec 2005, 5:30pm | ||
Okay, so we've got this christmas quiz thing at home. You'll have seen the like before - questions like "12 DOC" to which the answer is "Days of Christmas". Still quite a few left, so here we go... 4 CB 10 GB (HOTW) 2 SDMAS 9 LOAC 36 BKOAP 5 OR 3 MFASBE 18 TITP 30 MSIABUA 12 GMAT 4 PIAPT 2 WDMAR 10 DS 200 PFPG 3 FIOY 3 CIAF 22 TLD 26 LOTA 6 BIAO 7 DS 10 RP Any ideas? | ||
by Richard - Fri 21st Oct 2005, 3:18pm | ||
And just to keep you going here are a couple for base 8 (containing all of the numbers 1-7)**2 x * --- *** ** x *6 --- *** Both have unique solutions | ||
by Richard - Fri 21st Oct 2005, 1:00pm | ||
Richard said: base 5: (unique solution) Well, it's unique if you don't count swapping the two numbers being multiplied* x * -- ** | ||
by Richard - Fri 21st Oct 2005, 12:53pm | ||
base 5: (unique solution)* x * -- ** base 6: (unique solution) ** x * --- ** base 7: (2 solutions) ** x * --- xxx | ||
by Mike - Fri 21st Oct 2005, 9:27am | ||
Dubya said: Are there similar problems in other bases than base 10? OK: in base 4, the following contains all the digits from 1-3.* + 1 -- * Or is that not quite what you had in mind? | ||
by Dubya - Thu 20th Oct 2005, 10:12pm | ||
jpd said: OK, you asked for it - prove this is the only solution (or otherwise). Are there similar problems in other bases than base 10? | ||
by jpd - Thu 20th Oct 2005, 8:04am | ||
Richard said: Are there any other solutions? OK, you asked for it - prove this is the only solution (or otherwise). | ||
by Richard - Wed 19th Oct 2005, 11:54pm | ||
jpd said: The following multiplication contains all the digits 1-9. Fill in the blanks: 186 39 x ---- 7254 Are there any other solutions? | ||
by jpd - Wed 19th Oct 2005, 9:49pm | ||
Richard said: You could also start on any circle which is Is the right answer.1 + 1 / (2n*pi) miles north of the South pole. The following multiplication contains all the digits 1-9. Fill in the blanks: *** 3* x ---- **** | ||
by Richard - Wed 19th Oct 2005, 8:23pm | ||
jpd said: Is the right answer. You could also start on any circle which isIf we assume the small area around the South pole is flat, our start point would be any point on the circle which is 1 + 1 / (2 * pi) miles North of the South pole. Where else could I be? 1 + 1 / (2n*pi) miles north of the South pole. | ||
by Richard - Wed 19th Oct 2005, 7:48pm | ||
jpd said: Is that inclusive or exclusive? If it doesn't include 1, then I think 4&13 work.Peter is told the product, 52 Simon is told the sum, 17 52's factors are; 2&26, 4&13 Simon knows that Peter couldn't tell what the numbers were just from the product. If Simon was told 28, then one of the possibilities for 28 are 5&23, but the product of 5&23 is 115 (which can be made in no other way) - so if Simon was told 28, then he couldn't know that Peter couldn't tell what the numbers were. Therefore Simon was told the sum 17. Peter now knows what the numbers are. The possiblities for a sum of 17 are 2&15 (product 30), 3&14 (42), 4&13 (52), 5&12 (60), 6&11(66), 7&10(70), 8&9(72) product 30 gives 2&15(sum 17), 3&10(13), 5&6(11) Only a sum of 13 would be eliminated by Peter when told that Simon already knew that Peter couldn't tell what the numbers were (13 can also be 2&11 whose product 22 can only be formed in 1 way), leaving 2 remaining possibilities therefore Peter can't have worked out the right answer. Therefore it's not 2&15 as the answer. The same argument can be used for 42,60,66,70 and 72, but not for 52. Therefore Simon will also be able to work out that the numbers must be 4&13 | ||
by mjb - Wed 19th Oct 2005, 4:22pm | ||
jpd said: how can you possibly walk at the centre of the Earth? You obviously haven't read much Jules Verne then. | ||
by jpd - Wed 19th Oct 2005, 4:11pm | ||
Ingers said: I think of 2 integers between 1 and 100. Is that inclusive or exclusive? | ||
by Ingers - Wed 19th Oct 2005, 4:05pm | ||
Ok, this is an old chestnut, but is the single one of these sorts of problems that took me the longest time (and led to at least 1 man-day's loss of productivity at Deloitte). I think of 2 integers between 1 and 100. I tell Peter the Product and Simon the Sum. 1.) Peter: "I don't know what the numbers are" 2.) Simon: "I knew you wouldn't" 3.) Peter: "Now you've siad that, I do know" 4.) Simon: "Now you've said that I also know" What are the numbers? No computer programmes allowed | ||
by jpd - Wed 19th Oct 2005, 3:56pm | ||
mjb said: OK, so I rushed the previous one a bit. East is definitely undefined along the whole of the straight line that runs through the North and the South pole. Also, how can you possibly walk at the centre of the Earth?How aboot the centre of the earth, or is East undefined there as well. In which case, go out far enough such that your 1 mile East will take you back to where you started the Eastward leg. You are walking on the Earth's surface. And before you ask, no other form of transport is used. | ||
by Mike - Wed 19th Oct 2005, 3:53pm | ||
mjb said: How aboot the centre of the earth Have you suddenly turned Canadian? | ||
by mjb - Wed 19th Oct 2005, 3:51pm | ||
jpd said: Where else could I be? OK, so I rushed the previous one a bit.How aboot the centre of the earth, or is East undefined there as well. In which case, go out far enough such that your 1 mile East will take you back to where you started the Eastward leg. | ||
by jpd - Wed 19th Oct 2005, 3:41pm | ||
Rich said: At a position one mile north of the place where walking east around the south pole brings you in a full circle 1 mile in circumference, back to the same point. Is the right answer.If we assume the small area around the South pole is flat, our start point would be any point on the circle which is 1 + 1 / (2 * pi) miles North of the South pole. Where else could I be? | ||
by Rich - Wed 19th Oct 2005, 3:38pm | ||
jpd said: Also wrong. Aw, come on! You start "on the equator", you finish "on the equator"!!At a position one mile north of the place where walking east around the south pole brings you in a full circle 1 mile in circumference, back to the same point. | ||
by jpd - Wed 19th Oct 2005, 3:36pm | ||
Rich, using semantics said: On the equator? Also wrong. | ||
by Rich, using semantics - Wed 19th Oct 2005, 3:35pm | ||
jpd said: Good. Where else could you be? On the equator? | ||
by jpd - Wed 19th Oct 2005, 3:34pm | ||
mjb said: Also, depending on which north you take, you could be exactly 1 mile north of the South Pole. Is also the wrong answer (East is undefined at the South pole). | ||
by jpd - Wed 19th Oct 2005, 3:33pm | ||
mjb said: Anywhere exactly 2 miles north of the South Pole. Is the wrong answer. | ||
by mjb - Wed 19th Oct 2005, 3:31pm | ||
jpd said: Good. Where else could you be? Anywhere exactly 2 miles north of the South Pole.Also, depending on which north you take, you could be exactly 1 mile north of the South Pole. | ||
by mjb - Wed 19th Oct 2005, 3:28pm | ||
jpd said: How did you deduce that 3.16 was the "most likely" multiple of 0.79? because of the fives and zeros.jpd also said: If we don't spot this it's not too difficult to prove that the other three multiples of 79 (so 79, 158, 237) can't be an item value: they must all have two items with three fives (or 125) as a factor (we can't have four fives as the sum would be too large, and otherwise all three other item values would end in zero of five, which when summed with 79, 158 or 237 can't make a number ending in one). with 3,3,1,0.79 as a start point, multiplying one of 3,3,1 with a non-trivial number of pence would leave a partial pence result after the balancing division operation and a small pence multiplication would leave too large a result after division. but 5's and zeros are easy to come by in the pence column. | ||
by jpd - Wed 19th Oct 2005, 3:15pm | ||
Richard said: North pole? Good. Where else could you be? | ||
by jpd - Wed 19th Oct 2005, 3:13pm | ||
mjb said: Factorise 711 into 3,3,79. For addition, most likely multiple of 79 to use is 316, so we have 1,3,0.75,3.16 or similar. Then some guided trial and error to find the three smaller numbers. I wasn't this efficient. How did you deduce that 3.16 was the "most likely" multiple of 0.79?so 1,3,0.75 becomes 1,1,2.25 then 1.25,0.8,2.25 and eventually hits 1.25,1.2,1.5 which is the answer. I dealt entirely in pence, so the sum was 711 and the product 711 million. 711 million factorises easily into six twos, two threes, six fives and 79. Each item must have a value which is a product of the factors, with the four items using all factors. The item with 79 as a factor could only be 79 (on its own), 158 (with one two), 237 (with one three), 316 (with two twos), 395 (with one five), 474 (with a two and a three) or 632 (with three twos). All other possible combinations resulted in the item being worth more than 711. For the last three possible values (395, 474, 632) it is trivial to prove that the other factors cannot be combined to form a sum less than or equal to 711 for the last three. The minimum sum of item values for an item of value 316 is 710. Two of the item values for this minimum sum are 125 (which is 5 * 25) and 144 (which is 2 * 3 * 24); swapping the 5 with the (2 * 3) will obviously increase the sum by one to 711. If we don't spot this it's not too difficult to prove that the other three multiples of 79 (so 79, 158, 237) can't be an item value: they must all have two items with three fives (or 125) as a factor (we can't have four fives as the sum would be too large, and otherwise all three other item values would end in zero of five, which when summed with 79, 158 or 237 can't make a number ending in one). From here the number of potential item values is small enough to discount them easily for each of these three multiples of 79. We now know that one item is worth 316. We can easily discount having two items with three fives as factors as this would leave an item ending in an even number not ending in zero, so all three items must have at least one five as a factor and in fact two must have at least two fives as factors (otherwise we'd have to have an item with four fives as a factor which is too large). So our other three items have as factors five, 25 and 25. Since our known item value ends in six, our desired sum ends in one, and our other items all have five as a factor, we must have either one or three items ending in five. Any item with two and five as a factor will end in zero, so two of these items must have the four twos distributed between them. I'm sure you could continue like this but getting the answer through intuition at this point is trivial. | ||
by mjb - Wed 19th Oct 2005, 3:12pm | ||
Richard said: North pole? That seems to be the trivial answer. | ||
by Richard - Wed 19th Oct 2005, 3:09pm | ||
jpd said: North pole?I walk one mile South, one mile East and one mile North and end up where I started. Where am I? (obviously don't answer if I've posed this one to you before) | ||
by mjb - Wed 19th Oct 2005, 2:22pm | ||
mjb said something also making use of the fact that (not sure it this is generally true, but it works for these numbers)for a,b and x,y where x=a*f, y=b/f if a < x < b and a < y < b then (x+y) < (a+b) | ||
by jpd - Wed 19th Oct 2005, 2:17pm | ||
Mike said: I hope you're expecting more than one possible answer to this... I couldn't say how many answers I'm expecting. | ||
by mjb - Wed 19th Oct 2005, 2:16pm | ||
Mike said: Also out of interest, how did you do it? I'm wondering if my own method was hideously inefficient (even though I tried to make it logical rather than trial and error) Factorise 711 into 3,3,79. For addition, most likely multiple of 79 to use is 316, so we have 1,3,0.75,3.16 or similar. Then some guided trial and error to find the three smaller numbers.so 1,3,0.75 becomes 1,1,2.25 then 1.25,0.8,2.25 and eventually hits 1.25,1.2,1.5 which is the answer. | ||
by Mike - Wed 19th Oct 2005, 2:02pm | ||
jpd said: (Out of interest, how long did it take you?) Also out of interest, how did you do it? I'm wondering if my own method was hideously inefficient (even though I tried to make it logical rather than trial and error) |
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