Math Is Fun Forum

Hi Bobby,

Cross-number puzzles are number logic puzzles with clues/answers linked to each other, and it is up to the solver to work out which of them are so closely linked, and in which way, that something meaningful can be learnt from their association.

In the Introduction to his "Number Chains" book, Geoffrey R. Marnell writes:

Geoffrey R. Marnell's understanding of "a little logic" and "the logic required is uncomplicated" certainly differs from my understanding of them. He has a doctorate and is a Mensa member, whose puzzles have appeared in magazines and newspapers throughout the world.

As I see it, the Little Pigley Farm puzzle that I posted fits Marnell's description better than NOHOW, for which I used a little BASIC programming and some Excel to speed things up.

EDIT: I've since got Excel to do the part that I programmed in BASIC.

All I've ever needed for Marnell's puzzles and LPF are a calculator, a list of squares, cubes, quadruples and primes, paper, pen and a calculator...and some midnight oil! They're not easy!! But they are very satisfying to complete.

I still remember the feeling I got when I solved my first cross-number puzzle - which had done the rounds with my friends and was deemed to be too hard. It's easier than the two I've posted...maybe I should have started with that one, but I thought the members here would prefer something tougher. I might post it later, if Little Pigley and NOHOW go nowhere.

LG Horsefield in his "Cross-figure Puzzles" book gives some examples of strategy in a "Hints and Helps" section, but they're very simple. I could scan them and post the images if you like.

NOHOW is in a bit of a class and style of its own, as are other puzzles by Rhombus. Just making sense of the odd wording and working out what on earth he was getting at took me a while...but then I'm not the sharpest tool in the shed.

Yes...I sense that he is struggling with the deep concepts of this puzzle.

Hi Bobby,

I kept my tests down to these:

I wanted the biggest square of the form n² < 36, so if there were any other valid combinations that I could have ignored I would have.

You might have to enlighten this donkey, Bobby

Hi Bobby,

Only graphically, showing that other options deadend. I can't think of any other way.

Hi Bobby,

Same answer as dol88.

Hi Bobby,

I was always taught at school to use the 'squared symbol' for area calculations. My answer would have been 15000 cm².

No problem, Bobby...you left an opening for the teacher to explain that the correct answer is missing an important little something. But I won't say what (you know it), nor post it in that thread, in case the homework assignment isn't due to be handed in yet.

EDIT: I don't know how important it is these days, but my maths teacher was always a stickler for its inclusion and would dock marks if it was omitted.

Hi Bobby,

I tried that, but it didn't work for me.

I got together a finite list of uninteresting numbers, as you said to do, but failed to achieve a listing based on their uninterestingness as they were all equally uninteresting.

I'm sure that my lack of sleep from having stayed up half the night to watch the US Open tennis had nothing to do with that perception.

Finding that equally-boring group of numbers was probably just a fluke, but I wonder if (a) it is unique; or (b) there are a finite number of others; or (c) there are infinitely more such equally-boring groups.

I even considered listing them Every Which Way But Loose (starring Clint Eastwood) but dispensed with Every Which Way because of any preconceived notions I may have had that the number at the top (or bottom, or elsewhere) or left (or right, or elsewhere) - or any other Which Way - was of most interest, and so I went for Loose, listing them circularly in random order in an ever-spinning motion.

And, wouldn't you know it, after watching a few rounds of that the numbers were even more equally-uninteresting than before!

What is amazing about that, Bobby?

Hi Bobby,

I was going to say - before I saw your edit - that I've joined quittyqat's team.

I'm just waiting now for someone to comment about my comment that 1872653478596874152638476536475110010132 is incorrect.

Hi Bobby,

I decided against doing a practical coin test on that larger result found by your geometry program when I realised I'd have to stay up at least all night to do it...and I wanted to catch some of the US Open (live-streaming SopCast).

The threat of getting tenosynovitis from sending the smaller coin whizzing repeatedly around the larger one put me off too, as did having to find a calculator with a large enough mantissa to keep count...and I'd have to operate that with my other hand, unless I could devise some sort of sensor for it.

Keeping count mentally was, for me, quite out of the question (I'm not even mildly autistic)...once the number got too large to 'say' quickly the whizzing would slow down, eventually to less than a crawl, to the point where there wouldn't be enough time left for me to continue the test, as young as I might be right now.

Anyway, then I realised that 1872653478596874152638476536475110010132 was incorrect and switched on the tennis.

I wonder what your geometry program was looking for. I guess it thought that it found it, whatever it was, because it printed out the result. Or maybe all this spinning business was too much for its constitution...

For an integer solution I suppose the puzzle question could be extended with the addition of something like "and starting orientation" after "starting point".