Math Is Fun Forum

Numerically Challenged

Member

Registered: 2009-03-30

Posts: 3

No idea where to start

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)

smiyc86

Member

Registered: 2009-03-19

Posts: 78

Re: No idea where to start

---

I love Maths and Music ... dunno which more

Avon

Member

Registered: 2007-06-28

Posts: 80

Re: No idea where to start

I think you're right that starting and finishing aren't far apart.

integer

Member

Registered: 2008-02-21

Posts: 79

Re: No idea where to start

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.

Numerically Challenged

Member

Registered: 2009-03-30

Posts: 3

Re: No idea where to start

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)

Avon

Member

Registered: 2007-06-28

Posts: 80

Re: No idea where to start

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.

integer

Member

Registered: 2008-02-21

Posts: 79

Re: No idea where to start

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.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: No idea where to start

I'd guess those are clue numbers, not leading digits.

---

Why did the vector cross the road?
It wanted to be normal.

integer

Member

Registered: 2008-02-21

Posts: 79

Re: No idea where to start

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.

integer

Member

Registered: 2008-02-21

Posts: 79

Re: No idea where to start

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...

Numerically Challenged

Member

Registered: 2009-03-30

Posts: 3

Re: No idea where to start

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)