1. ## A weary traveller

I was on holiday the other month,travelling on a lone road through the forest of Anifbocci (in Italy) when I came across a river which had a number of stepping stones. From behind a bush an old man jumped out. "Be not afraid weary traveller but for you to cross this river, you must answer these three questions"

Always up for a challenge I said " Please proceed, dear bridge keeper" and this is what he explained.

In fact there was not just one set of stepping stones but three. The first set consisted of just 3 stones (set 1), the second set of 5 stones set 2) and the last group 15 stones (set 3). The old man explained to me that I was able to cross the river by either stepping on to the next stone or else hop over one stone to land on the next and could be done as many times as I wanted in any one journey. To clarify it he used the example as if there were only two. (for this one the answer is two because you can step/step or hop/step)

1) "What is the maximum number of combinations you need to cross set 1?"
2) "What is the maximum number of combinations you need to cross set 2?"
3) "What is the maximum number of combinations you need to cross set 3?"

Of course I told him the answer "Hip, hip hooray, you may pass" and I did.

Now my question, having answered questions 1- 3
4) Can you find the clues to the answer in my question?" (clue: there are 3 and RudiS likes these)........ <img src=/S/whisper.gif border=0 alt=whisper width=29 height=17> Rudi, nothing personal, just another cryptic clue

2. ## Re: A weary traveller

Careful how you use cryptic clues Jezza. The lounge will hip hop all over you if the cryptic clue does not have a logical singular answer! I have learned the hard way! <img src=/S/smile.gif border=0 alt=smile width=15 height=15>

3. ## Re: A weary traveller

Jezza,

I am a little confused by your example. If there are 2 stones (as well as the two river banks) then surely there are 3 possibilities:
1. <LI>step - to stone 1, step - to stone 2, step - to the other bank
<LI>step - to stone 1, hop - to the other bank
<LI>hop - to stone 2, step - to the other bank
Have I misunderstood?

StuartR

4. ## Re: A weary traveller

Rudi,

Give us another chance and we can give you one <img src=/S/smile.gif border=0 alt=smile width=15 height=15>. Multiple answers is OK, but you have to accept any valid one, see for example how <!profile=bandido>bandido<!/profile> dealt with an unexpected (but valid) response in <post#=428001>post 428001</post#>

StuartR

5. ## Re: A weary traveller

My apologies,

The bridge keeper being a lonely hermit sometimes got confused. What he should have said was.... " Starting from the first step in each set"

Hopefully this image should help his explanation.

6. ## Re: A weary traveller

Very helpful, but I reckon he must be suffering from inattention, because when he said
<hr>To clarify it he used the example as if there were only two. (for this one the answer is two because you can step/step or hop/step)<hr>
He really meant the answer is two because you can step/step or hop

Anyway, here is my answers for sets 1 and 2, I'm still thinking about set 3, but it's a very big number...
<UL><LI>Set 1 (3 stones) <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Three Combinations: step/step/step, hop/step, step/hop</span hide>
<LI>Set 2 (5 stones) <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Seven Combinations: step/step/step/step/step, hop/step/step/step, hop/hop/step, hop/step/hop, step/hop/step/step, step/hop/hop, step/step/step/hop</span hide>[/list]StuartR

7. ## Re: A weary traveller

Hi Stuart

A bit more work on the 5 stones. The last one is a step up on the numbers but I will give you clue to assist you

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold"> a lone road, Anifbocci and Hip, Hip Hooray </span hide>

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold"> It help you to not get mixed up </span hide>

8. ## Re: A weary traveller

Understood! <img src=/S/brainwash.gif border=0 alt=brainwash width=15 height=15>

9. ## Re: A weary traveller

I don't understand the clues at all, but I reckon that 15 stones has a total of <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">40163</span hide> possibilities. The calculation went a bit like this (but don't ask me to justify it...)

<table border=1> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Hops</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Steps</td></span hide> <td align=center valign=top></td></span hide> <td align=center valign=top></td></span hide> <td align=center valign=top></td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">0</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">15</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold"></td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold"></td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">1</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">1</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">13</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">14! / 13!</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">14</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">14</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">2</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">11</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">13! / 11!</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">13 * 12</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">156</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">3</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">9</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">12! / 9!</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">12*11*10</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">1320</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">4</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">7</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">11! / 7!</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">11 * 10 * 9 * 8</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">7920</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">5</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">5</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">10! / 5!</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">10 * 9 * 8 * 7 * 6</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">30240</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">6</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">3</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">9! / 6!</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">9 * 8 * 7</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">504</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">7</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">1</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">8! / 7!</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">8</td></span hide> <td valign=top><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">8</td></span hide> </table>
StuartR

10. ## Re: A weary traveller

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold"> Anagram - "Anifbocci" and "Hip" and "a lone road" they may give you a clue to a well known accumulation of numbers!</span hide>

11. ## Re: A weary traveller

<img src=/S/yikes.gif border=0 alt=yikes width=15 height=15> This is not a puzzle anymore...this is a higher grade science exam question.

There must be a more down to earth answer????

Jezza, whats up with this, 'cos I'm <img src=/S/bagged.gif border=0 alt=bagged width=22 height=22>

12. ## Re: A weary traveller

With that clue:
5 stones: <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">8 possibilities</span hide>
15 stones: <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">987 possibilities</span hide>

13. ## Re: A weary traveller

Well done Hans <img src=/S/whisper.gif border=0 alt=whisper width=29 height=17> had a feeling you'd get it

14. ## Re: A weary traveller

Hi Rudi

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">This was a two threaded puzzle. What happens is the number of hop/steps increases in a sequence. After getting the first 2 or 3 you will then start seeing a well known sequence of numbers. 1,1,2,3,5,8....... this is know as the Fibonacci sequence.

The hidden anagrams were

"a lone road" - Leonardo as Leonardo Da Vinci was a well known "user" of the numbers in his Art and Science
"Anifbocci"- Fibonacci
"Hip"- Phi this will take too long to explain but go to http://goldennumber.net (I have purposely not set the link to this as it will show through the hidden text)</span hide>

15. ## Re: A weary traveller

Thanx for the details Jezza. I'm into cryptics, but I would never have attempted this. My brain only has two modes: Easy and Forget about it! I should maybe a apply for a <img src=/S/newbrain.gif border=0 alt=newbrain width=21 height=22> with Smiley!!!

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