Mathematical Thinking I, II, .... (previously Puzzle: Marrie

[S.H.]

I'm never good at giving riddles, anyway.. 


You arrive at a hotel and have 3 sets of golden rings. The first set of rings has 4 rings, the second set has 2 rings and the third only has one ring. You cannot take these sets of rings apart, exchange them for a different form of currency, and the hotel clerk has no change. You want to stay at the hotel for 7 nights, and you have to pay one gold ring for each night that you stay. You cannot pay in advance, or all at once at the end of your stay. How do you pay for your 7 nights at the hotel?

[Holmes]

Spoiler:

The 1st night give the clerk the single gold ring.
The 2nd night give the clerk the double gold ring and he will give you the single gold ring back as change.
The 3rd night give the clerk the single gold ring.
The 4th night give the clerk the 4 gold rings and he will give you the double and single gold rings back as change.
The 5th night give the clerk the single gold ring.
The 6th night give the clerk the double gold ring and he will give you back the single ring as change.
The 7th night give the clerk the single gold ring.

And also, with this method, you don´t leave tips! 

If it is correct ...
Next question:

Reason why 30414093201713378043612608166064768844377641568960512078291027000 cannot possibly be the value of 50 factorial, without actually performing the calculation.

It can be esasy, but also difficult.

[S.H.]

Spoiler:

The 1st night give the clerk the single gold ring.
The 2nd night give the clerk the double gold ring and he will give you the single gold ring back as change.
The 3rd night give the clerk the single gold ring.
The 4th night give the clerk the 4 gold rings and he will give you the double and single gold rings back as change.
The 5th night give the clerk the single gold ring.
The 6th night give the clerk the double gold ring and he will give you back the single ring as change.
The 7th night give the clerk the single gold ring.

And also, with this method, you don´t leave tips! 

If it is correct ...

Yup, it is correct 

Next question:

Reason why 30414093201713378043612608166064768844377641568960512078291027000 cannot possibly be the value of 50 factorial, without actually performing the calculation.

It can be esasy, but also difficult.

Spoiler:

Because among the 50 factorial, there are 50, 40, 30, 20, 10 or 5x10,4x10,3x10,2x10,1x10   so that means there are at least 5 zeros at the end like 12300000 .. (excluding the 2*5 also equal to 10 etc....But wont need it anyway..) That's why   3041409320171337804361260816606476884437764156896051207829........1027000 cannot be possibly be the value of 50 factorial

By the way, I miss your LT. 


Edit: Forgot to answer in spoiler...Sorry

[Holmes]

need another Problem S.H, you got it right.

[S.H.]

Don't think this is counted as a mathematical riddle though..

There are 4 men crossing the bridge. (Yup..bridge again..) The conditions are :
The bridge can only be crossed by at most two people.
They need a flashlight to cross the bridge and they have only 1 flashlight.(That means 2 person will cross the bridge with the flashlight and 1 must return with it.)

They use different amount of time to cross the bridge.
Man A can cross the bridge in at most 1 minute.   
Man B can cross the bridge in at most 2 minutes.   
Man C can cross the bridge in at most 5 minutes.   
Man D can cross the bridge in at most 10 minutes.   


Question: What is the shortest time possible for them to cross the bridge? How?

[chubs191]

Spoiler:

19 minutes.
Man A crosses the bridge first with man D- 10 min
Man A returns with the flashlight- 1 min
Man A takes man C across the bridge- 5 min
Man A yet again returns with the flashlight- 1 min
Man A takes man B across the bridge- 2 min

And everyone is across, YAY!
Man A must be exhausted.

[c-square]

Spoiler:

19 minutes.
Man A crosses the bridge first with man D- 10 min
Man A returns with the flashlight- 1 min
Man A takes man C across the bridge- 5 min
Man A yet again returns with the flashlight- 1 min
Man A takes man B across the bridge- 2 min

And everyone is across, YAY!
Man A must be exhausted.

There's a faster way (and one in which Man A gets a break!)

Spoiler:

Man A and B cross together - 2 mins
Man A returns with the flashlight - 1 min
Man C and D cross together - 10 mins
Man B returns with the flashlight - 2 mins
Man A and B cross together - 2 mins

Total time: 17 minutes

Next:

101 - 102 = 1

Move one digit to make this equation true.

Note:  You can only move one digit.  You can't have digits exchange places or mess with the minus or equals sign.

[S.H.]

Spoiler:

19 minutes.
Man A crosses the bridge first with man D- 10 min
Man A returns with the flashlight- 1 min
Man A takes man C across the bridge- 5 min
Man A yet again returns with the flashlight- 1 min
Man A takes man B across the bridge- 2 min

And everyone is across, YAY!
Man A must be exhausted.

Not correct, try again. 

Spoiler:

Man A and B cross together - 2 mins
Man A returns with the flashlight - 1 min
Man C and D cross together - 10 mins
Man B returns with the flashlight - 2 mins
Man A and B cross together - 2 mins

Total time: 17 minutes

Yup. That's it

By the way, can give an example of "You can only move one digit.  You can't have digits exchange places or mess with the minus or equals sign."  Can't understand it..Sorry 

[chubs191]

Ah man! These are always harder than they seem.  I should go back to elementary school, high school is frying my brain! 

[c-square]

By the way, can give an example of "You can only move one digit.  You can't have digits exchange places or mess with the minus or equals sign." 

Sure.  

Starting equation: 101 - 102 = 1

So, you could move the two so it's like this:

1201 - 10 = 1

or move the second zero so it's like this:

101 - 12 = 10

or move the last one so it's like this:

1011 - 102 =
(Though that doesn't make much sense as there's nothing on the right side of the equals sign)

Or if you really wanted to, move the first one down and to the right so it's like this:

01 - 102 = 1                                                      

                                                      1

Of course, none of the above examples are the correct answer.  :)

           

[chubs191]

I might just be really oblivious but...

Spoiler:

Are you sure this isn't like a matchstick problem, where you move the top/ bottom of the equal sign to the minus sign to make it 101=102-1

Because I did all the possible solutions and none of them come close to fitting.
(Click the other spoiler sign to see the long list)

Spoiler:

101-102=-1

011-102=-91
110-102=8
11-0102
11-1002=-991
11-1002
11-1020=-1009
11-102

011-102
011-102
01-1102=-1001
01-1102
01-1012=-1011
01-1021=-1020
01-102=-101

110-102
110-102
10-1102=-1092
10-1102
10-1012=-1002
10-1021=-1011
10-102=-92

1101-02=1099
1101-02
1011-02=1010
1011-02
101-012=89
101-021=80
101-02=99

0101-12
1001-12=989
1001-12
1010-12=998
101-012
101-120=-19
101-12

2101-10=2091
1201-10=1191
1021-10=1011
1012-10=1001
101-210=-109
101-120=-19
101-10=91

[c-square]

I might just be really oblivious but...

Are you sure this isn't like a matchstick problem, where you move the top/ bottom of the equal sign to the minus sign to make it 101=102-1

Because I did all the possible solutions and none of them come close to fitting.
(Click the other spoiler sign to see the long list)

Spoiler:

101-102=-1

011-102=-91
110-102=8
11-0102
11-1002=-991
11-1002
11-1020=-1009
11-102

011-102
011-102
01-1102=-1001
01-1102
01-1012=-1011
01-1021=-1020
01-102=-101

110-102
110-102
10-1102=-1092
10-1102
10-1012=-1002
10-1021=-1011
10-102=-92

1101-02=1099
1101-02
1011-02=1010
1011-02
101-012=89
101-021=80
101-02=99

0101-12
1001-12=989
1001-12
1010-12=998
101-012
101-120=-19
101-12

2101-10=2091
1201-10=1191
1021-10=1011
1012-10=1001
101-210=-109
101-120=-19
101-10=91

Nope.  You're not allowed to change the minus or equals sign.  You can only move a digit.

As for your list, I'm not sure where you're getting these nines and eights from.  There are just two zeros, four ones and a two to work with.  And there are possibilities that you haven't considered, though you kind of have to think outside the box.  (One of my examples is a subtle hint!)  Although this question is definitely mathematical, it also requires some lateral thinking.

[Sayumi]

How about this:

Spoiler:

101-10²=1

[c-square]

How about this:

Spoiler:

101-10²=1

You got it!

Your turn to put up a puzzle.

[Holmes]

The Big Return of Sayumi