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Hi All,
I was hoping some of you clever folk could lend me afew pointers in how to solve this cross number puzzle.
I don't even know where to start and once started, who knows I might even be able to complete myself, but I'm thinking that starting and finishing aren't that far apart.
1 X X X 2
X X
X 3 X X X 4
X X X X
5 X X X X X
X X
6 X X X X
Across
1. (4 down/2)-17569
3. (5 across - 2488)/3
5. (2 down -60,000)x5
6. (3 across x 2)-2618
Down
1. (3 across x 6) - (6 across x 2)
2. 6 across + 5 across
3. (6 across/2)+2332
4. (3 across x 7)+257
Many Thanks
Numerically Challenged
Last edited by Numerically Challenged (2009-03-30 22:31:13)
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I love Maths and Music ... dunno which more
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I think you're right that starting and finishing aren't far apart.
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Across
6. (3 across x 2)-2618
3xxx4 * 2 = ????8 - 2618 = ????0 <--last digit is a zero
Down
4. (3 across x 7)+257
3xxx4 * 7 = ????8 + 257 = ????5 <--last digit is a five
Seems inconsistent.
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Thanks to those of you who have replied I've now made a start and am a little closer, (couldn't be any further anyway!), But I did forget to mention leading zeros are allowed
eg 00123 = 123
Last edited by Numerically Challenged (2009-04-01 17:31:02)
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But I did forget to mention leading zeros are allowed
It doesn't matter. The clues define a linear system with eight equations and eight unknowns that has a unique solution. You don't need to know that the answers fit together in the grid, or that they are integers.
This is a very unusual cross-number puzzle.
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But I did forget to mention leading zeros are allowed
eg 00123 = 123
Based on the clues it is IMPOSSIBLE to have a leading zero.
You have already specified the first digit of all the numbers.
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I'd guess those are clue numbers, not leading digits.
Why did the vector cross the road?
It wanted to be normal.
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I'd guess those are clue numbers, not leading digits.
OK.
abcde--
f---g--
h-ijklm
n-o-p-q
rstuv-w
--x---y
--záíóú
Using the clues above, fill in the numbers for the letters.
Simple enough.
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In the following:
a1 means 1 across; a3 means 3 across; etc.
d1 means 1 down; d2 means 2 down; etc.
a1 is defined in terms of d4.
a1 [LHS] points to or refers to d4 [RHS]
or [in my notation]
a1 -> d4
d4 -> a3
a3 -> a5
a5 -> d2
d2 -> a5 & a6
a5 already refers to d2 -- self ref
a6 -> a3
a3 -> a5
a5 already refers to d2 -- self ref
This enters a self referencing loop.
That implys that a5 or d2 can be isolated.
Therefore, substituting, expanding and simplifying
an exact number is determined.
If you need further assistance...
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Many thanks to all those who have contributed and especially to Integer who posted a solution that I could properly understand (I'm referring to the hidden text)
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