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

Posts: 49
Re: Mathematical Thinking I, II, .... (previously Puzzle: Ma
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?
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?

 Erabareshi Kodomotachi
Posts: 1291
Re: Mathematical Thinking I, II, .... (previously Puzzle: Ma
[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.[/spoiler]
And also, with this method, you donÂ´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.
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.[/spoiler]
And also, with this method, you donÂ´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.
Last edited by Holmes on April 26th, 2009, 12:13 pm, edited 1 time in total.

Posts: 49
Re: Mathematical Thinking I, II, .... (previously Puzzle: Ma
Holmes wrote:[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.[/spoiler]
And also, with this method, you donÂ´t leave tips!
If it is correct ...
Yup, it is correct
Holmes wrote: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[/spoiler]
By the way, I miss your LT.
Edit: Forgot to answer in spoiler...Sorry
Last edited by S.H. on April 26th, 2009, 10:54 pm, edited 1 time in total.

 Erabareshi Kodomotachi
Posts: 1291
Re: Mathematical Thinking I, II, .... (previously Puzzle: Ma
need another Problem S.H, you got it right.

Posts: 49
Re: Mathematical Thinking I, II, .... (previously Puzzle: Ma
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?
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?

 Queen of Randomness
Posts: 151
Re: Mathematical Thinking I, II, .... (previously Puzzle: Married?)
[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.[/spoiler]
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.[/spoiler]
Grammar Nazis Unite (GNU)
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 Shounen Tantei Dan, Dai Seikou!
Posts: 1040
Re: Mathematical Thinking I, II, .... (previously Puzzle: Ma
chubs191 wrote:[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.[/spoiler]
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[/spoiler]
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.
Last edited by csquare on May 2nd, 2009, 7:07 pm, edited 1 time in total.
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Posts: 49
Re: Mathematical Thinking I, II, .... (previously Puzzle: Ma
chubs191 wrote:[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.[/spoiler]
Not correct, try again.
csquare wrote:
[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[/spoiler]
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
Last edited by S.H. on May 2nd, 2009, 10:53 pm, edited 1 time in total.

 Queen of Randomness
Posts: 151
Re: Mathematical Thinking I, II, .... (previously Puzzle: Ma
Ah man! These are always harder than they seem. I should go back to elementary school, high school is frying my brain!
Grammar Nazis Unite (GNU)
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 Shounen Tantei Dan, Dai Seikou!
Posts: 1040
Re: Mathematical Thinking I, II, .... (previously Puzzle: Ma
S.H. wrote: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. :)
Last edited by csquare on May 3rd, 2009, 6:20 am, edited 1 time in total.
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 Queen of Randomness
Posts: 151
Re: Mathematical Thinking I, II, .... (previously Puzzle: Married?)
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=1021
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]
[spoiler]101102=1
011102=91
110102=8
110102
111002=991
111002
111020=1009
11102
011102
011102
011102=1001
011102
011012=1011
011021=1020
01102=101
110102
110102
101102=1092
101102
101012=1002
101021=1011
10102=92
110102=1099
110102
101102=1010
101102
101012=89
101021=80
10102=99
010112
100112=989
100112
101012=998
101012
101120=19
10112
210110=2091
120110=1191
102110=1011
101210=1001
101210=109
101120=19
10110=91
[/spoiler]
[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=1021
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]
[spoiler]101102=1
011102=91
110102=8
110102
111002=991
111002
111020=1009
11102
011102
011102
011102=1001
011102
011012=1011
011021=1020
01102=101
110102
110102
101102=1092
101102
101012=1002
101021=1011
10102=92
110102=1099
110102
101102=1010
101102
101012=89
101021=80
10102=99
010112
100112=989
100112
101012=998
101012
101120=19
10112
210110=2091
120110=1191
102110=1011
101210=1001
101210=109
101120=19
10110=91
[/spoiler]
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 Shounen Tantei Dan, Dai Seikou!
Posts: 1040
Re: Mathematical Thinking I, II, .... (previously Puzzle: Ma
chubs191 wrote: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=1021
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]101102=1
011102=91
110102=8
110102
111002=991
111002
111020=1009
11102
011102
011102
011102=1001
011102
011012=1011
011021=1020
01102=101
110102
110102
101102=1092
101102
101012=1002
101021=1011
10102=92
110102=1099
110102
101102=1010
101102
101012=89
101021=80
10102=99
010112
100112=989
100112
101012=998
101012
101120=19
10112
210110=2091
120110=1191
102110=1011
101210=1001
101210=109
101120=19
10110=91[/spoiler]
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.
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Posts: 124
Re: Mathematical Thinking I, II, .... (previously Puzzle: Married?)
How about this:
[spoiler]
10110Â²=1[/spoiler]
[spoiler]
10110Â²=1[/spoiler]
"It is one of those instances where the reasoner can produce an effect which seems remarkable to his neighbor, because the latter has missed the one little point which is the basis of the deduction."
Sherlock Holmes
Sherlock Holmes

 Shounen Tantei Dan, Dai Seikou!
Posts: 1040
Re: Mathematical Thinking I, II, .... (previously Puzzle: Ma
Sayumi wrote:How about this:
[spoiler]10110Â²=1[/spoiler]
You got it!
Your turn to put up a puzzle.
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 Erabareshi Kodomotachi
Posts: 1291
Re: Mathematical Thinking I, II, .... (previously Puzzle: Married?)
The Big Return of Sayumi