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DenmarkKilo wrote:
800/10304 would be more correct. Which is 7.8% (rounded up)

...... is the correct answer .

See, I knew you lot were far more intelligent than Doctor Jones from down the road.

Just for the record:
here's a link to a full explanation of the puzzle

......... and on with the next riddle

You have 3,000 carrots and a donkey which can carry at most, 1,000 carrots at a time.
The donkey eats a carrot before moving a unit.
You want to transport the carrots 1,000 units.

Note: you can move back and forth, dropping carrots along the way and picking them up on your way back (just remember though, that you can never carry more than 1000 carrots at a time).
..... and note that moving backwards a unit, still requires the donkey to eat a carrot.

So, for example, you could pick up 1000 carrots, move ..... say 300 units, drop 400 carrots and then just have enough carrots to get you back to the start to pick up some of the remaining 2000 carrots.

So:
What is the maximum number of uneaten carrots that you can move 1,000 units?

Assume that the donkey can only move in whole numbers of units and can only consume whole numbers of carrots - no fractions allowed !!!!

Let me give this a first try. Since he has to eat at least one carrot to move a unit, and have at least one per unit to return and pick more carrots, I would try to find the furthest the donkey can go that would leave it with 1000 carrots to finish the distance.
So:
To reach 400 units the donkey has to eat 800 carrots (to come and go) and it could drop 200 carrots at 400units assuming we load it with the max 1000 carrots
The second time is the same. So the donkey is back in the beginning. There are 400 carrots at 400units distance and 1000 at the beginning. We load the donkey with the remaining 1000 so it reaches the 400 unit mark with 600 carrots, we pick up the rest 400. So we have 1000 carrots to cover 600units and so the donkey finishes with 400 carrots.

Nightfall wrote: and so the donkey finishes with 400 carrots.

The actual answer is between 500 and 600, so 400 is not a bad first attempt .

Anyone wanna try and better 400 ???

No takers ????

moonbeam wrote:

Nightfall wrote: and so the donkey finishes with 400 carrots.

The actual answer is between 500 and 600, so 400 is not a bad first attempt .

Anyone wanna try and better 400 ???

532 carrots?

501? 502? 503? 504? 505? 506? 507? 508? 509? 510? 511? 512? 513? 514? 515? 516? 517? 518? 519? 520? 521? 522? 523? 524? 525? 526? 527? 528? 529? 530? 531? 533? 534? 535? 536? 537? 538? 539? 540? 541? 542? 543? 544? 545? 546? 547? 548? 549? 550? 551? 552? 553? 554? 555? 556? 557? 558? 559? 560? 561? 562? 563? 564? 565? 566? 567? 568? 569? 570? 571? 572? 573? 574? 575? 576? 577? 578? 579? 580? 581? 582? 583? 584? 585? 586? 587? 588? 589? 590? 591? 592? 593? 594? 595? 596? 597? 598? 599?

Part-Timer wrote:

moonbeam wrote:

Nightfall wrote: and so the donkey finishes with 400 carrots.

The actual answer is between 500 and 600, so 400 is not a bad first attempt .

Anyone wanna try and better 400 ???

532 carrots?

Soooooooooooooooooo close ....... you're prob on the right track - I think I know where you went wrong. Explain your answer and I'll show you where you went wrong (plus others may wanna see the solution too ).

Believe it or not - Stoner has the correct answer .

Woo-hoo!!!

moonbeam wrote:Soooooooooooooooooo close ....... you're prob on the right track - I think I know where you went wrong. Explain your answer and I'll show you where you went wrong (plus others may wanna see the solution too ).

I was in a bit of a hurry, so didn't want to post the working if I'd managed to confuse myself thoroughly. I had a feeling I might have gone slightly wrong at one stage.

My first attempt ended exactly like Nightfall's answer. As I knew that was wrong, I left it (places to go...).

I came back and theorised that, the further the donkey travels before its first "drop-off point", the more carrots it eats on the journey out and the journey back. So, I took it to the opposite extreme, and started working out what would happen if the donkey went only one unit of distance before dropping off a batch of carrots.

It came to this: To go one unit of distance, with the whole batch of carrots, takes 5 carrots. Pick up 1000, eat one, drop off 998, keeping one more to eat on the way back. Pick up 1000, drop off 998, go back for the last 1000 carrots. Travel one unit, leaving you one unit away from the start, with 2995 carrot left.

You keep repeating this process until you have gone 200 units of distance. At this point, 1000 carrots have been consumed (200 x 5). For the next stage, each unit of distance only costs 3 carrots, because you now only need to make two trips instead of three (you have 2000 carrots left).

Ahh. I did indeed go wrong at the point I thought I did! Something didn't feel quite right about the uneven division at this stage. The catch is that the donkey eats a carrot before moving, isn't it?

So, what should happen is to divide 999 by 3 (the number needed to carry two maximum loads of carrots), giving 333. At 533 units of distance along, you have 1001 carrots. You feed the donkey one carrot, then move the 1000 one unit. You then use up 467 more carrots, getting to the end of your journey with 533 carrots left.

Believe it or not - Stoner has the correct answer .

The deuce, you say!

Part-Timer wrote:At 533 units of distance along, you have 1001 carrots. You feed the donkey one carrot, then move the 1000 one unit. You then use up 467 more carrots, getting to the end of your journey with 533 carrots left.

You're nearly correct - but you forgot that when you fed the donkey one carrot - it moved along one unit:

At 533 units of distance along, you have 1001 carrots. You feed the donkey one carrot, then move the remaining 1000 carrots one unit.
you then use up 466 more carrots (you are now at the 534 unit mark), getting to the end of your journey with 534 carrots left.

534! I said that!

moonbeam wrote:You're nearly correct - but you forgot that when you fed the donkey one carrot - it moved along one unit:

At 533 units of distance along, you have 1001 carrots. You feed the donkey one carrot, then move the remaining 1000 carrots one unit.
you then use up 466 more carrots (you are now at the 534 unit mark), getting to the end of your journey with 534 carrots left.

I had a feeling there should have been yet another carrot, as I thought I must have used two too many when I went wrong the first time. Oh well, I'd probably have got there on the third go!

Still, the Stoner got it right, so it must be his turn to set a puzzle.

and i thought magic was nerdy!

IAIN wrote:and i thought magic was nerdy!

And you were right.