Thinking on Boxing Day - difficult but solvable puzzles

[Jonathan Rogers]

I have been pondering over various puzzles over the last few days. Then, I had some kind of epiphany on a bus today when I solved two of them in my head within minutes of each other. See how you compare

1) a chessbase puzzle - construct a game which White wins by playing 6 gxf8 = N mate. There is only one possible solution. If you have a line where move order doesn't always matter, you have already gone wrong.

2) a puzzle (among many) sent by my Essex team captain - and it's maths now: a x bc = def. Each of these letters represents a different one of the numbers between 1-6. Which is which? (Or of you prefer, how do you multiply a single digit number by a double digit number to get a three digit number, using each digit from 1-6 once?)

[JustinHadi]

I have been pondering over various puzzles over the last few days. Then, I had some kind of epiphany on a bus today when I solved two of them in my head within minutes of each other. See how you compare

1) a chessbase puzzle - construct a game which White wins by playing 6 gxf8 = N mate. There is only one possible solution. If you have a line where move order doesn't always matter, you have already gone wrong.

2) a puzzle (among many) sent by my Essex team captain - and it's maths now: a x bc = def. Each of these letters represents a different one of the numbers between 1-6. Which is which? (Or of you prefer, how do you multiply a single digit number by a double digit number to get a three digit number, using each digit from 1-6 once?)

On 2) the digit 1 must be in def (I think!, quick trial and error)

EDIT and probably 5 must be b c or d as well.

[Jonathan Rogers]

Yes, you're on your way.

I wish I had started there!

[Richard Bates]

1) Being a Kings indian player might help! Used to Knights ending up in strange places...

[JustinHadi]

I can do 2) but not 1) time to take up the King's Indian...

[IM Jack Rudd]

I've solved (2), but have not yet proved uniqueness.

[JustinHadi]

The question assumes uniqueness but it can be proved via elimination if nothing else.

[Geoff Chandler]

Got one (well half remembered it). The h1 Rook figures in the solution.
There is a guy on RHP who sets all kinds of these retro puzzles, this one included.

He drive me mad. I keep saying I won't look, I won't bother and
yet I soon find myself spending ages looking at the bloody thing.

No idea about number two.

[Alistair Campbell]

The h1 Rook figures in the solution.

Not in my "solution"...

[Jonathan Rogers]

Not?! Pray do tell!

Together, Richard and Geoff have provided very helpful clues.

[Alistair Campbell]

Oops - mine was 6. exf8=N mate. Always read the question. Apologies. As you were...

[Jonathan Rogers]

As a matter of curiosity, how do you get there with 6 exf8 =N mate?

[Simon Brown]

Thanks for these Jonathan. 2 didn't take long when I worked out where 5 and 1 had to be. 1 took much longer as I couldn't envisage a position which had a unique move order, but I have it now. If you want a clue, Jonathan should give it but I suggest giving Black's first move.

[Richard Bates]

As a matter of curiosity, how do you get there with 6 exf8 =N mate?

I can see a couple of solutions, each i think with their own unique move orders, one involving 1...e6 and 1...e5 (otherwise basically equivalent). It's a shame because (assuming no other solutions) it would otherwise make just as nice a puzzle as the original question.

[IM Jack Rudd]

As a matter of curiosity, how do you get there with 6 exf8 =N mate?

I can see a couple of solutions, each i think with their own unique move orders, one involving 1...e6 and 1...e5 (otherwise basically equivalent). It's a shame because (assuming no other solutions) it would otherwise make just as nice a puzzle as the original question.

Just to check the solutions are the same as the ones I'm thinking of - the queens are on d5 and h4, right?