The Maths Thread
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Tommy_Catons_Perm
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I this python script? I don't know it. I only knew BASIC and FORTRAN 77 at one time.
I didn't think about an infinite number of possible answers. Does it work with any multiplier?
There's a really unimpressive intuitive way you can do it.
You know the number ends in 9, and you know it's going to be multiplied by 4, so the new number will end in a 6 (as 9x4=36). The 3 can be carried for later (Technically it's 30).
So we know the old number ends in 69.
We've already multiplied the 9, so if you multiply the 60 (as 69=60+9) by 4 you get 240. Add the 30 carried from earlier and you get 270. The 2 can be carried like the 3 before (Technically it's 200).
So we know the new number ends in 76, and thus the old number ends in 769.
We've already multiplied the 69, so we multiply the 700 by 4 and get 2800. Add the 200 and we get 3000. So our next digit is 0. We carry the 3 (again technically it's 3000)
So we know the new number ends in 076, and thus the old number ends in 0769.
We've already multiplied the 769, so we multiply the 0 (as 0x1000=0) by 4 and get 0. Add the 3000 carried and we get 3000. So our next digit is 3. Nothing carried.
So we know the new number ends in 3076, and thus the old number ends in 30769.
We've already multiplied the (0)769, so we multiply the 30000 by 4 and get 120000. Nothing to add so the next digit is 2. Carry the 1 (blah blah 100000)
So we know the new number ends in 23076, and thus the old number ends in 230769.
We've already multiplied the 30769, so we multiply the 200000 by 4 and get 800000. Add the 100000 and we get 900000. So our next digit is 9.
So we know the new number ends in 923076, and thus the old number ends in 9230769. But this last number is irrelevant. (Unless we wanted a larger number that satisfied the answer)
The new number is 923076 is 4 times 230769, and satisfies the question.
So the smallest answer is 230769.
Apologies if the code above is pretty much what I said. I can't read it too well.
You know the number ends in 9, and you know it's going to be multiplied by 4, so the new number will end in a 6 (as 9x4=36). The 3 can be carried for later (Technically it's 30).
So we know the old number ends in 69.
We've already multiplied the 9, so if you multiply the 60 (as 69=60+9) by 4 you get 240. Add the 30 carried from earlier and you get 270. The 2 can be carried like the 3 before (Technically it's 200).
So we know the new number ends in 76, and thus the old number ends in 769.
We've already multiplied the 69, so we multiply the 700 by 4 and get 2800. Add the 200 and we get 3000. So our next digit is 0. We carry the 3 (again technically it's 3000)
So we know the new number ends in 076, and thus the old number ends in 0769.
We've already multiplied the 769, so we multiply the 0 (as 0x1000=0) by 4 and get 0. Add the 3000 carried and we get 3000. So our next digit is 3. Nothing carried.
So we know the new number ends in 3076, and thus the old number ends in 30769.
We've already multiplied the (0)769, so we multiply the 30000 by 4 and get 120000. Nothing to add so the next digit is 2. Carry the 1 (blah blah 100000)
So we know the new number ends in 23076, and thus the old number ends in 230769.
We've already multiplied the 30769, so we multiply the 200000 by 4 and get 800000. Add the 100000 and we get 900000. So our next digit is 9.
So we know the new number ends in 923076, and thus the old number ends in 9230769. But this last number is irrelevant. (Unless we wanted a larger number that satisfied the answer)
The new number is 923076 is 4 times 230769, and satisfies the question.
So the smallest answer is 230769.
Apologies if the code above is pretty much what I said. I can't read it too well.
Tommy_Catons_Perm
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I just did
4 x 9 = 36.
4 x 6 + 3 = 27
4 x 7 + 2 = 30
4 x 0 + 3 = 03
4 x 3 + 0 = 12
4 x 2 + 1 = 09
Stop
Final number = 923076 (read last digit in lines above).
This is the same explanation as above but without all the words and the zeros !
4 x 9 = 36.
4 x 6 + 3 = 27
4 x 7 + 2 = 30
4 x 0 + 3 = 03
4 x 3 + 0 = 12
4 x 2 + 1 = 09
Stop
Final number = 923076 (read last digit in lines above).
This is the same explanation as above but without all the words and the zeros !
Don't talk to me or my son ever again.
My son is at MMU in his second year of a Maths degree. He worked out the script above using a program called Matlab. It worked out the first solution pretty quickly. It took him about half an hour to come up with that.
We changed the first line to x = 230770 and his laptop was too slow to find another solution. He wants a faster computer for Christmas.
The explanations above are sound also. I came up with the same first solution using this method, but in the old long division style. The second solution of 230,769,230,769 came by extending the same method.
We changed the first line to x = 230770 and his laptop was too slow to find another solution. He wants a faster computer for Christmas.
The explanations above are sound also. I came up with the same first solution using this method, but in the old long division style. The second solution of 230,769,230,769 came by extending the same method.
Everyday maths in our local shop. True story.
Me: Do you sell stamps?
Her: Yes, they come in books of 12.
Me: l'll take 48 please
Her: Total blank
Me: Thats 4 books.
Her: Oh, that's clever.
Me: (thinks, don't say a word)
Me (stupidly) 4 times 12 is 48.
Her: (vaguely) Right.
Me: Do you sell stamps?
Her: Yes, they come in books of 12.
Me: l'll take 48 please
Her: Total blank
Me: Thats 4 books.
Her: Oh, that's clever.
Me: (thinks, don't say a word)
Me (stupidly) 4 times 12 is 48.
Her: (vaguely) Right.
TheRemainsOfTheDave
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They are. I'm a programmer and would just have looped from 1 up to a result where the result meets the criteria being the leftmost number of the result equals 9 and the rightmost number of the seed is 9. A mix of mathematics and string parsing.