Math Is Fun Forum

Hi Bobby,

Yes, 41 is possible: 8 + 17 + 12 + 4 = 41

Here's how I got them all:

I used T&E to find the six numbers.

I think 1, 2, 4 & 8 are essential for the first four numbers, and a central 1, surrounded by 8 > 2 > 4, gives the highest score: 11.

So that gives 12 (or something lower) for the fifth number.

12 succeeds right up to 19, and I then tested for the sixth number, starting with 28 (one greater than the sum of the other numbers) and working down. 17 is the first one that works up to the sum of all six numbers.

I doubt that number 1 would succeed anywhere but in the centre, as probably all the other numbers need access to it at some stage or other, which would not be possible if it were placed on the outer ring.   

I wonder what the max is.

I tried it with 1,2,4,8,16,32 but couldn't do it. The best I got was 44, using these numbers:

Hi! This is my imposter here.

Nice! That works perfectly.

It's the senior version of the junior version I used to find my first answer

This is the largest answer my calculator can handle:

Used the copy/paste functions! And I didn't bother typing in the comma delimiters this time!

Oh. I was just in the middle of typing out all the other decimal-place versions of that number when I saw your post.

Are there more answers than the one in my first post? I can't see how there could be.

Found one so far:

Hi Bobby,

From the thread title it looks as if we're being asked to provide the clue.

Anyway, I know this one...and it's not too easy to spot!

Hi Bobby,

I can understand the interest some have in trying to solve one of these puzzles by programming and the use of formulas and functions, as I had that too until I realised it was all too hard for me. It's a great challenge, and there's the ultimate satisfaction if successful , but also the absolute frustration if unsuccessful!

These puzzles generally just need a calculator and some logic to solve, and are aimed at the general populace - but only those who enjoy doing number puzzles, of course! I actually get more pleasure from just taking time out from the computer and sitting down in the lounge room with one of these puzzles. Then (particularly with these older puzzles), it's just me versus the puzzle setter...on equal footing. Pen, paper and calculator.

I often use Excel or BASIC to help with other puzzles...and that's fun too!

Ooo - we're off and running, Bobby!

Sorry, but I can't keep up with much of that. I don't know Maple or Mathematica at all (or any other such programs) - other than messing around a bit with the clever Mathematica solution someone gave me to my Joan's telephone number and my YOB puzzle.

Sit's article is quite a few years old, and may well be outdated.

He is very conversant with crossnumber puzzles and has commented on several - including Little Pigley Farm and NOHOW. He even constructed his own - Lucas-Bonaccio Farm, 1998 - which he "presented to the Math Club at City College on April 24, 1998". That puzzle is beyond me (I've tried...and failed). I might try it again sometime, but according to Sit it "requires a combination of logic, number theory, computing and programming skills, trigonometry, trial and error, and of course, some knowledge about farming".

I'm not defending him, of course...just trying to give you some more (worthless?) background info you may not know.

Dr. Rainer Typke has an online solver at http://www.crossnumber.com/. You can choose from a selection of puzzles submitted by members and solve them online, but you need to register before you can enter a puzzle of your own.

Sit's quote is from the article published on Typke's site (I recall seeing it there many years ago), and in that article Sit also comments on Typke's solver program.

I've entered several puzzles on Dr. Typke's site over the years...including More or Less. For anyone constructing such puzzles the solver is a good means of testing for uniqueness, as it will show all solutions.

I bought Dr. Typke's book "Cross Number Puzzles" that contains 30 good puzzles and has some tips on solving strategies for this genre.

Hi Bobby,

I only saw your solution to #1 just now, so I'll stop my little brute force Excel spreadsheet program. I was getting close to melting my cpu, anyway!

I'd just passed 2,600,000 (had starting with zero) for the test value of b (no solutions, of course), and still had quite a way to go before reaching b's maximum test value of 18,257,418 (after that, 3b²+3b+7 comes to more than Excel's 15 digit max.)

I was too lazy to try to work out a better brute force option, but it would have gone the same way...nowhere.