[itachi-san]

Every morning, a monk walks up the steps to his temple. First, he climbs up to the middle step and meditates for 1 minute. Then he climbs up 8 steps and faces east until he hears a bird singing. Then he walks down 12 steps and picks up a pebble. He takes one step up and tosses the pebble over his left shoulder. Now, he walks up the remaining steps three at a time which only takes him 9 paces. How many steps lead up to the temple?

[Guest]

But 4 can be the correct answer for a noun because there are 4 vertical rises, and that is precisely what constitutes a step--a vertical rise in otherwise horizontal flooring. And I understand how 3 could also be accepted as an answer for a noun (although not for a verb, which makes 4 even more fitting), but I'm still clueless as to how you can conceive 5 steps. Imagine it this way...

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If that is the first vertical rise, and you count the area in front of it as a step (which you would to reach 5 steps), that means you are counting the entire ground level as a step.

[Guest]

The answer is 49 without a doubt. Itachi used this as a riddle during ABR 4-2. But here's the reason:

In order to have an exact "middle step" you have to have an odd number of steps to begin with. So, with 49 steps, the middle step is going to be 25. So...Starting at 25 he takes 8 steps up to step 33. After hearing the bird he takes 12 steps down to step 21. He picks up the pebble and steps up one step to step 22. He throws the pebble over his shoulder and steps up 3 steps at a time a total of 9 times. 3x9=27. So he was at step 22 and goes up a total of 27 steps to end the top being step 49.

[Guest]

The answer is 49 without a doubt. Itachi used this as a riddle during ABR 4-2. But here's the reason:

In order to have an exact "middle step" you have to have an odd number of steps to begin with. So, with 49 steps, the middle step is going to be 25. So...Starting at 25 he takes 8 steps up to step 33. After hearing the bird he takes 12 steps down to step 21. He picks up the pebble and steps up one step to step 22. He throws the pebble over his shoulder and steps up 3 steps at a time a total of 9 times. 3x9=27. So he was at step 22 and goes up a total of 27 steps to end the top being step 49.

I think the verb vs noun debate is really steps vs. stairs.

If you believe that there are 5 steps in the diagram, then 49 is the solution.

If you believe that there are 4 steps, then 48 is the solution

If you say there are 3 steps, then 49 will leave you on the top step - short of the temple.

I can see interpreting the number of steps as 3 or 4, but I don't think 5 is reasonable. Nobody counts both the first floor and second floor as steps in a staircase.

Therefore, my money is on 48.

[Guest]

I understand your logic and accept your answer as correct under one interpretation, but 48 is also a correct answer based on xucam's diagram. I feel I have argued strongly enough in support of it's validity to have 48 accepted as also being correct. As often occurs in the Brainden, multiple answers will arise that are both correct and can be proven with valid reasoning.

[Jiminy Cricket]

How do you reach 5? By my count (and past experience), that setup would cause me to raise my feet up a step 4 times (4 vertical rises). Even if you count the 'flats' at steps, the step cannot begin until the vertical rise, so there are 4 flats following vertical rises.

I could see a case for 3 steps (because the top and bottom would be the floors) but I feel counting the vertical rises is the most accurate way to count steps, and that diagram clearly has 4.

You are standing on step X.

You can take two steps up X+1, X+2

You can take two steps down X-1, X-2

If you are, as you say, standing on the second step then if you took one step down you would be on the first step, yeah?

If you were then standing on the first step and took one step down would you say you were standing on the zero step?

The puzzle stems from you counting the total number of steps.

You say 48 I say 49 because I'm counting the total number of steps as counted from both directions.

Going up the top landing is a step up.

Going down the bottom landing is a step down.

It could be argued that your diagram shows only three steps and two landings.

[Guest]

But that's precisely my point. You can't count 5 because "going up" and "coming down" are different directions, and though the movement of the person walking is up and down, the landings are crossed in only 1 direction, which means one of them must be counted as a step.

And I do not refute the point that you can label the diagram as 3 steps and 2 landings. I was just saying that under your argument of 'noun' versus 'verb', 4 steps fits under both headings, whereas 3 steps only fits as a noun

[Guest]

Every morning, a monk walks up the steps to his temple. First, he climbs up to the middle step and meditates for 1 minute. Then he climbs up 8 steps and faces east until he hears a bird singing. Then he walks down 12 steps and picks up a pebble. He takes one step up and tosses the pebble over his left shoulder. Now, he walks up the remaining steps three at a time which only takes him 9 paces. How many steps lead up to the temple?

do you really want me to answer this?

Itachi, Can you see how many ways this could have gone? Ha and none of the answers were mine!

Edited December 4, 2008 by crazypainter

[Guest]

You are standing on step X.

You can take two steps up X+1, X+2

You can take two steps down X-1, X-2

If you are, as you say, standing on the second step then if you took one step down you would be on the first step, yeah?

If you were then standing on the first step and took one step down would you say you were standing on the zero step?

The puzzle stems from you counting the total number of steps.

You say 48 I say 49 because I'm counting the total number of steps as counted from both directions.

Going up the top landing is a step up.

Going down the bottom landing is a step down.

It could be argued that your diagram shows only three steps and two landings.

Sure, three steps and 2 landings is one interpretation, in which steps is synonymous with stairs.

And it takes you 4 steps to get from the bottom to the top or from the top to the bottom.

there is just no way to count that as 5 steps!

But, if you count that as 5 steps, then your answer of 49 is correct (for some values of correct).

If you count it as 4 steps, the answer is 48

But if you count it as 3 steps, the answer is 47?

The middle step is then 24.

8 up takes you to 32

12 down takes you to 20

one up takes you to 21

Then you climb 3 at at time: 24, 27,30,33,36,39,42,45,48 (Temple level!)

Since the top step is 47, the upper landing would be step 48 - but by this definition of steps it is not, and although you went up the same distance as 3 steps, you only climbed 2 steps.

So 47 doesn't work, if'n you're being pedantic.

IMHO regardless of which way you are going, the steps are this set : ( L, 1, 2, 3, ..., L ]

The destination landing, since it takes a step to reach, is included. The landing of origin is not included. Ergo 4. Ergo 48.

[Guest]

I think we must agree to disagree on this one. No one is wrong. Now everybody hug & be friends

[Guest]

32 steps

x=(8-12)+1)+(9*3)

[Guest]

32 steps

x=(8-12)+1)+(9*3)

that is 24 not 32

and you start in the middle so you have to double it so you must be in the 48 camp

Edited December 4, 2008 by HokieKen

[Jiminy Cricket]

I think we must agree to disagree on this one. No one is wrong. Now everybody hug & be friends

I hope nothing I said was taken personally or as an attack.

I thought I was simply discussing the puzzle.

I apologize if my comments offended anyone.

[Guest]

I hope nothing I said was taken personally or as an attack.

I thought I was simply discussing the puzzle.

I apologize if my comments offended anyone.

Certainly none taken here at all! I just wanted to be clear that I wasn't trying to tell anyone else that they were wrong and I don't believe anyone else had that intention either I think it's been a great discussion and I love simple puzzles with more than one answer!

[Guest]

The only offense I took was in the inherent falsehoods of your argument --purely kidding of course. We both had valid points that were well argued.

As for this hugging matter, we aren't a support group, so I'll pass

[Guest]

I hope nothing I said was taken personally or as an attack.

I thought I was simply discussing the puzzle.

I apologize if my comments offended anyone.

Likewise!

[Guest]

Just a thought semanticly ....... while treading carefully

If it was the stairway to heaven. How many treads would he have trod on?

off topic .... Anyone remember the film the thirtynine steps?