Crossword Help Forum
Forum Rules

Am I right in thinking that the cells landed on would include the top of a snake but not the bottom, and vice versa for ladders?

No, Ozzy, the other way round. The final resting place after the move. So bottom of snake after you’ve slid down it and top of ladder after you’ve climbed it. I can’t imagine your way would work to give 10 digits

Thank you Quisling, but I think they both give ten cells - you just substitute top for bottom and vice versa.

By all means try it your way and see if you come up with a solution, but I don’t think it’s the natural way to read the preamble or how the game works. Effectively you are saying your next move starts in a different cell from the one on which your last move finished, if I have understood you.

Also apologies, if I had read the example in the preamble I wouldn't have needed to ask!

I was confused by the preamble referring to "landing" at the foot of a ladder or at the head of a snake. But the example is clear.

I have only just started this puzzle but thought I would try as an experiment using Chat GPT instead of a calculator.
The response to the instruction “Make a complete list of all 10 digit numbers that can be produced by raising a two digit prime number to the power of any prime number” produced a short list of all options in a few seconds.
It feels like cheating but is it any different to using a spreadsheet?

Prompted by the last post, I tried ChatGPT and it asked me to install Python (which I haven't yet done ...) so I tried 3 of the other big AI's: Microsoft CoPilot, Google Gemini and Anthropic Claude. CoPilot produced rubbish initially but with a slight tweak produced the right answers. Gemini produced several answers quickly, 2 of which were wrong (!) - giving the correct formula but the incorrect calculation of it. And it also missed one other answer ... Claude couldn't cope with this at all, produced two or three wrong answers even with tweaks to the prompt. An interesting exercise in comparing Ai's.

I have just put exactly the same question into copilot using GPT-5 and got exactly the same answer.
I typed it into a google search box in Safari and Apple AI jumped in and again gave exactly the same answer.
I assume it is right but can’t be sure as I have not done it with a spreadsheet.
Chat GPT justified the answer with this comment pasted below
“ Why this is complete (brief): for each two-digit prime p the maximal exponent q that can produce a number < 10^{10} is \lfloor\log_{p}(10^{10}-1)\rfloor. I checked all prime exponents up to that limit for every two-digit prime; only the eight pairs above produced values in the 10-digit range.”
Maybe the precise wording is important. I tried first and missed out the second “prime” in the instruction and nearly broke the internet. It failed and told me it needed too much computing power to do on my subscription.
I am aware AI needs to be used with great caution but the potential power is really exciting.

Also interested in how AI answers - plenty of wrong ones, Grok counted commas so gave me 11 digits. Once scolded - list of "2 digit primes raised to a prime" arrived at second attempt. Used this to confirm I was on the right track. How others do these numericals without excel beats me. I used cell background colours to highlight the snakes and ladders and the cells landed on, without this aid my eyes could not cope. As I only do the numericals I have just noticed the address to send the answer to has changed, no longer St Albans, when did this happen?