Another Puzzle

[cloudee1]

Alright no one asked, but I can explain this one.

Dealing with the first and last numbers, we have three options,

1XXX3 2XXX6 3XXX9

We know this because X[sub]1[/sub] cannot be bigger than 3 or X[sub]5[/sub] will be a two digit number, same in that X[sub]2[/sub] cannot be larger than 5 or X[sub]4[/sub] will be too large.

Now to the other three digits, again there are only three options,

X529X X418X X307X

Because X[sub]2[/sub] cannot be less than 3 or X[sub]3[/sub] will be negative.
The reason that we only looked at those two numbers is that all other numbers can be derived from them, according to given statement.

X[sub]5[/sub] = 3X[sub]1[/sub]
X[sub]3[/sub] = X[sub]2[/sub] - 3
X[sub]4[/sub] = X[sub]2[/sub] + 4

So now we just look for the combination that answers the question, Which has three pairs which add up to 11, our choices

15293 =1 pair 25296=3 pair 35299=2 pair
14183 =1 pair 24186=0 pair 34189=1 pair
13073 =0 pair 23076=0 pair 33079=0 pair

25296

[Neo]

Heres another different sort of puzzle

A recent murder case centered around the six men, clarke, fllip, grahm, hunt, mark, and walt. In one order or another these man were the victim, the murderer,the witness, the police, the judge, and the hangman. The facts of the case were simple. The victim had died instantly from the effect of gunshot wound inflicted a shot. After a lengthy trial the murderer was convicted, sentenced to death, and hanged.

1 Mark knew both the victim and the murderer.
2 In court the judge asked clarke to give his account of the shooting.
3 Walt was the last of the six to see fllip alive.
4 The police testified that he picked up grahm near the place where the body was found.
5 Hunt and walt never met.
What role did each of the following play in this melodrama ?
a) Murderer
b) Victim
c) Judge
d) Witness

Ok this one gives me too many possibilites can anyone give me the right one.

[Candy]

1 Mark knew both the victim and the murderer.

Mark was neither the victim nor the murderer (so, 4 open), but wasn't the hangman or the judge either (they didn't see the victim). Only the police and the witness both qualify.

2 In court the judge asked clarke to give his account of the shooting.

Easy, who would have seen the shooting? -> Clarke is the witness

4 The police testified that he picked up grahm near the place where the body was found. (this one first, 3 doesn't give enough hint if done before this one)

If Grahm was picked up by the police, he WASNT the police. Picking up can be two things, the literal one (he was victim) or the logical (he was the murderer), so he wasn't any of the other four.

3 Walt was the last of the six to see fllip alive.

There were two deaths. If Walt was the last to see Fllip alive, he must've murdered him. Walt thus is either the murderer, or the hangman.

Fllip and walt cannot be victim + murderer (grahm must be one of them), so they must be murderer and hangman. Walt is hangman, Fllip is murderer.

Grahm only could be the victim at this point.

Now, there's only Mark and Hunt to complete, for Judge and Police. Mark knew both, so he was the police, and Hunt was the Judge.

Check for 5:

5 Hunt and walt never met.

Judge & hangman don't meet. By definition.

Conclusion:

Grahm was murdered by Fllip. Clarke saw the thing, called in Mark to police the area. Fllip was led before Hunt, who convicted him of murder and he was subsequently hung by Walt.

Good night

[Neo]

A cyclist is cycling in a circular path.he is at some point on the path,at that point 1/5th of the cyclists infront of him and 5/6th back of him gives the total number of cyclists participating in the race.
What is the total number of cyclists?