Math Is Fun Forum

384...xlnt!

I've shaved some moves from mine, too! Down by 22 to 413 (L5 & L6). Nice to reduce L6's cricket score...but not down to yours yet.

Haven't looked at your paths...don't want to spoil the fun or challenge of trying to work it out myself.

I've updated our scores in my previous post.

Btw, Jane, I feel rather mean about this thread taking over from yours...especially after seeing your lonely post there re your good L3 score. Pity we can't splice threads.

Hi Bobby,

Yes, I should have shown fractions. I was going to but didn't think to use improper fractions, and as MIF only provides the "½" fraction symbol I opted to display my answer with the recurring digits after the decimal point. I could've tried LaTeX, but this was easier and I didn't realise the two modes gave different results.

WolframAlpha's "decimal approximation" of the fractional input is exactly the same as the one given by my calculator for which I used decimal input...up to WolframAlpha's maximum output of 3705 digits. Maybe it can display more digits, but I didn't know how to get it to do that (my calculator displays up to 5012 digits).

I wonder what the actual difference is between the correct answer and the approximations given by both WolframAlpha and my calculator.

I used Excel to solve both parts: spreadsheet for 'b' and Solver for 'a'.

Btw, your 'hidden text' label shows "b" instead of "a".

Nothing to do with typing speed...

...with my free hand I was able to pick up the cup of tea that I knocked off the desk just as it hit the floor - all without spilling a drop.

Btw, I don't know how you would have known about my exceptionally-quick manual dexterity.

Hi cberry,

After getting nowhere with trying to find a solution to your problem I googled it and found

Hi Bobby,

What you may not be aware of is that during the 16 minutes and 50 seconds that it took me to reply to your post I made and drank a hot cup of tea even before reading what you wrote. I also typed my post one-handed with one finger, as it was early morning here and my other hand was fast asleep. So was most of the rest of me...except for my brain, which was barely ticking along on autopilot just pre-bedtime.

Hi Bobby,

The 'digital root' option didn't work out, and so I've deleted reference to it.

Oh, yes...I see. I hadn't understood that point until now.

I think

I had to remove negative test numbers from my original program because I was getting incorrect mod results (eg, that -14 mod 9 = -5, instead of 4); and I didn't know how to fix that without too much messing around that I shouldn't have to do. Excel did it correctly (answer 4...same as WolframAlpha).

My output table of solutions and their remainders made it easy to analyse and work out the formula that I mentioned earlier. Testing x,y = 0 to 100 made the pattern obvious.

Btw, the formula I gave in post #21 was simply derived from observations that I made from a list of results produced with x,y values ranging from -100 to 100 for each variable.

I used BASIC to find x,y answers within that range that satisfied ZHero's "X*Y is congruent to X+Y mod 9" problem and then printed the list.

I did it in

They were the easy ways for me.

Hi Bobby,

The two ways are equally clear to me. For problems that lend themselves to that approach I prefer to go that way because I use my scientific calculator a lot and like to try to find concise methods to suit calculator entry if possible.

Made a meal of that one! Your answer explains it well.

Hi Bobby,

If they all ran at the same speed as each other for the whole race, then

If they each maintained their own speed for the whole race then

Hi John,

I use SnagIt for video captures...and also for general screen captures. There are many such programs available - some freeware - and I've tried several. SnagIt suits me best and has many features that I like (eg, captures scrolling windows; good annotation tools). It costs, but it's very reliable and I enjoy using it - which is quite often.
 

Yes, it's very cleverly done! Some diamonds are tricky to get, and you can even get stuck with no escape (other than by pressing "Ctrl").

Once you get the hang of it you'll find that the 1024-move limit is quite generous.

My fewest moves:
Level 1: 12
Level 2: 53
Level 3: 23
Level 4: 31
Level 5: 51
Level 6: 71
Level 7: 19
Level 8: 57
Level 9: 42
Level 10: 76
Total: 435