Boing Boing posted this puzzle (have a look or the rest of this post will be meaningless). Being lazy I wrote a little program to determine all the possible solutions to the equation a.b.c = 225 expecting to be given a single answer, unfortunately that didn’t happen and six possible solution sets were returned.
Of all 6 solutions these first three seem most likely :
ages[1,3,75] house number = 79
ages[1,5,45] house number = 51
ages[1,9,25] house number = 35
these next 3 solutions seem less likely as the olddest person in the house would normally be an adult :
ages[1,15,15] house number = 31
ages[3,5,15] house number = 23
ages[5,5,9] house number = 19
Can anyone see what I’m missing in the question which would allow the census taker to know with absolute certainty their ages? Obviously he has the advantage of knowing the house number and being able to make a good guess at the age of the door answerer but beyond that I’m stumped.
And then Dan said:
Ok, maybe this doesn’t make sense, but from the numbers you’ve given…
The specified “oldest” of his question assumes that there was some confusion when he learned the other figures. Perhaps knowing the number of the house narrows it down to a couple of possible answers from the ones you point out.
But then he asks the question “Which is the oldest”, which proves to him that there is actually one who is the oldest. Presumably this narrows the choice down to being 5, 5, and 9, as there’s nothing to choose between the younger ones and there’s only one who is oldest.
Does that actually work? Maths isn’t at all my forte, but it seems to be the only reason for asking the question after looking up at the number of the house. This means that there must be another series of numbers that work out to 19 as being the number of the house… but I can’t work that out because I’ve been in the pub.
Sorry.
And then Dan said:Also, your redesign doesn’t have a “Little Things” top title to click on to take readers back to your main site; you have to go post by post. Otherwise, I like the minimalist black and white.
Sorry again.
And then tom said:the design is still on progress, at the moment I’m just seeing how much stuff I can throw out from the default template and still have things work… as for the puzzle, i think you may be right, i’ll modify the program so it can tell us all possible ways reather than assuming possible houses with the same house number must be made of the same ages
And then tom said:OK so here’s the full list
No. 79 : 1, 3, 75
No. 51 : 1, 5, 45
No. 35 : 1, 9, 25
No. 31 : 1, 15, 15
No. 35 : 1, 25, 9
No. 51 : 1, 45, 5
No. 79 : 1, 75, 3
No. 79 : 3, 1, 75
No. 31 : 3, 3, 25
No. 23 : 3, 5, 15
No. 23 : 3, 15, 5
No. 31 : 3, 25, 3
No. 79 : 3, 75, 1
No. 51 : 5, 1, 45
No. 23 : 5, 3, 15
No. 19 : 5, 5, 9
No. 19 : 5, 9, 5
No. 23 : 5, 15, 3
No. 51 : 5, 45, 1
No. 35 : 9, 1, 25
No. 19 : 9, 5, 5
No. 35 : 9, 25, 1
No. 31 : 15, 1, 15
No. 23 : 15, 3, 5
No. 23 : 15, 5, 3
No. 31 : 15, 15, 1
No. 35 : 25, 1, 9
No. 31 : 25, 3, 3
No. 35 : 25, 9, 1
No. 51 : 45, 1, 5
No. 51 : 45, 5, 1
No. 79 : 75, 1, 3
No. 79 : 75, 3, 1
…the only house number that can be made in two different ways is 31, 15+15+1 and 25+3+3 so i guess we have to assume that in the bizaro land of this question that two people who are 15 are exactly the same age. In reality it’s possible for two people to be 15 and one of them two be older than the other. So I recon the question is rubbish.
And then Dan said:Actually, maybe it’s not even that complicated. The puzzle doesn’t actually ask a question. Perhaps the trick is in realising that it’s just a statement.
It would certainly have saved some time.
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