Maths Puzzle

The following puzzle was posted on one of the departmental forums...

ABCDEF x G=BCDEFA

We know that:

ABCDEF is even
G is odd
All are different digits

Being as it's the computing department a few people have brute forced this but, given that I'm ill today, I thought I'd have a go at solving it properly - and succeeded!

Here goes....

1) For ABCDEF to be even, F must be even.

2) Even x odd = even so BCDEFA must be even, so A is even.

3) All are different digits so ABCDEF can't be equal to BCDEFA, so G does not equal 1.

4) ABCDEF has the same number of digits as BCDEFA so, A x G must be less than 10.

5) Possible options for A and G are: A ∈ {0, 2, 4, 6, 8}, G ∈ {3, 5, 7, 9}. Given that found in 4), A must be in {0, 2} as 3x4=12. Including a leading zero is rather unlikely, so A = 2.

6) Given 5) and 4), G = 3. So now we have:
2BCDEF
x 3
-----------
BCDEF2
------------

7) 3 x F ends in 2, given that F is even, 3 x F ∈ {0, 12, 18, 24}. F must be 4. So now we have:
2BCDE4
x 3
-----------
BCDE42
------------

8) (3 x E)+1 ends in 4, so 3 x E ends in 3. E can be either odd or even so 3 x E ∈ {0, 3, 15, 18, 21, 24, 27}, therefore E = 1.
2BCD14
x 3
-----------
BCD142
------------

9) 3xD ends in 1. D can be odd or even so 3 x D ∈ {0, 15, 18, 21, 24, 27}, therefore D = 7.
2BC714
x 3
-----------
BC7142
------------

10) (3 x C)+2 ends in 7, so 3 x C ends in 5. C can be either odd or even so 3 x C ∈ {0, 15, 18, 24, 27}, therefore C = 5.
2B5714
x 3
-----------
B57142
------------

11) (3xB)+1 ends in 5, so 3 x B ends in 4. B can be odd or even so 3 x B ∈ {0, 18, 24, 27}, therefore B = 8.
285714
x 3
-----------
857142
------------

Note, once I'd got A and G I did initially start by trying to solve this from the other side as follows (I quickly realised that I'd got the wrong end!):

7) The value of B must be at least 6 (AxG plus any carry over values). Therefore, B ∈ {6, 7, 8, 9}.

8) Given that 3 x B ∈ {18, 21, 24, 27}, some carry over value will be applied so the value of B must be greater than 6. Therefore, B ∈ {7, 8, 9} and 3 x B ∈ {21, 24, 27}.

9) Given 8), the carry over must be 2. So B is greater than or equal to 8, B ∈ {8, 9}. (Note, the obvious thing to do here is say that B ∈ 8, but it's possible for B to equal 9... take for example the value 298145 x 3 = 917435).

Film in Four Words (Prince Caspian)

Much better than Wardrobe.

(Image from Liberty Film Festival, more film info at IMDB)

I was very pleasantly surprised by this film. Having seen The Lion, The Witch and The Wardrobe at the cinema almost as soon as it came out and been really quite disappointed, I totally expected this to be awful but felt obliged to watch it anyway. Having waited until it reached the university cinema I was really quite surprised at how un-rubbish this film actually was. A vast improvement and enjoyable.

Friday Fill-In

This week's Friday Fill-In:

1. Follow the leader.

2. Books are something I always take with me on vacation. (Towels and pyjamas are the things I always forget!)

3. To achieve your goals, you must know what you want

4. "I always appreciate gifts of Cadbury's Dairy Milk" is something I'd like you to know about me.

5. I have a cold.

6. Coca-Cola floats. I've never had one and I can't imagine I'd like them at all!

7. And as for the weekend, tonight I'm looking forward to projecting at the cinema, tomorrow my plans include the Big Gig! and Sunday, I want to get a bit of sleep!

Wizard of Oz

I've just been doing a very quick bit of research into the Wizard of Oz approach to usability studies (by which I mean checking it meant what I thought it did) and somehow ended up at Wikipedia's page on Political Interpretions of the Wonderful Wizard of Oz. I have a feeling I've seen some of this before and promptly forgotten it all, but it's amazing that:

1) People can draw so much out of all these things. Whether it's on religious grounds or political it seems that something like this exists for almost any kids story, classical novel or well-known film (and probably some lesser known ones too). Maybe I'll have to go looking for some more but there's always the classic Lord of the Rings religious arguments :) Even on the poetry front I sometimes have to wonder how much of the subtleties and double meanings were *really* intended and how many just worked out that way - did people really write all those GCSE anthology poems with so many meanings?

2) That people can contribute so many details to Wikipedia :) It's strangely addictive.

Teaser Tuesdays: Pyramids (Terry Pratchett)

TEASER TUESDAYS asks you to:

• Grab your current read.
• Let the book fall open to a random page.
• Share with us two (2) “teaser” sentences from that page, somewhere between lines 7 and 12.
• You also need to share the title of the book that you’re getting your “teaser” from … that way people can have some great book recommendations if they like the teaser you’ve given!
• Please avoid spoilers!

My 2 “Teaser” Sentences for today:

“It is astonishingly difficult to walk with legs full of straw when the brain doing the directing is in a pot ten feet away, but he made it as far as the wall and felt his way along it until a crash indicated that he'd reached the shelf of jars. He fumbled the lids of the first one and dipped his hand gently inside.”

Page 256 of Pyramids by Terry Pratchett

Paddington!

(Image from today's Google search page)

Tehe, Paddington Bear is awesome.

Film in Four Words (Corpse Bride)

Fantastic music. Dark. Pretty.

(Image from BFI, more film info at IMDB)

Tim Burton, Johnny Depp and Danny Elfman makes a good combination. I'm not quite sure I don't prefer Nightmare Before Christmas but it's a tough call.