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puzzle, solve by equations
Clash Royale CLAN TAG#URR8PPP
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Recently I got this puzzle and I was able to solve it but brute force iteration method..( trail and error iteration). I'm wondering is it possible to come-up with like a equation which on solving will give the same answers?
Puzzle:
One person had a habit of spending money according to dates.
I.e. If date is 19 he was spending Rs.19 and if date is 15, he was spending Rs. 15.One night he calculated total spending of 5 consecutive days – Monday to Friday and he found that he spent Rs. 61 in 5 days.
Ans : Feb, 27, 28 Mar 1,2,3
puzzle
asked Aug 21 '16 at 7:35
Venkat.V.S
142
migrated from stats.stackexchange.com Aug 21 '16 at 9:37
This question came from our site for people interested in statistics, machine learning, data analysis, data mining, and data visualization.
add a comment |Â
up vote
0
down vote
favorite
Recently I got this puzzle and I was able to solve it but brute force iteration method..( trail and error iteration). I'm wondering is it possible to come-up with like a equation which on solving will give the same answers?
Puzzle:
One person had a habit of spending money according to dates.
I.e. If date is 19 he was spending Rs.19 and if date is 15, he was spending Rs. 15.One night he calculated total spending of 5 consecutive days – Monday to Friday and he found that he spent Rs. 61 in 5 days.
Ans : Feb, 27, 28 Mar 1,2,3
puzzle
asked Aug 21 '16 at 7:35
Venkat.V.S
142
migrated from stats.stackexchange.com Aug 21 '16 at 9:37
This question came from our site for people interested in statistics, machine learning, data analysis, data mining, and data visualization.
Is the answer correct? That totals to Rs. 61.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Aug 21 '16 at 9:41
Something's funky here, I can't even see the puzzle.
– Oscar Lanzi
Aug 21 '16 at 9:58
sorry the total is 61
– Venkat.V.S
Aug 23 '16 at 7:35
I tried 5x+10=61, 4x+7=61, 3x+6=61, 2x+7=61. The last one gave me the solution.
– blackpen
Aug 28 '16 at 23:30
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Recently I got this puzzle and I was able to solve it but brute force iteration method..( trail and error iteration). I'm wondering is it possible to come-up with like a equation which on solving will give the same answers?
Puzzle:
One person had a habit of spending money according to dates.
I.e. If date is 19 he was spending Rs.19 and if date is 15, he was spending Rs. 15.One night he calculated total spending of 5 consecutive days – Monday to Friday and he found that he spent Rs. 61 in 5 days.
Ans : Feb, 27, 28 Mar 1,2,3
puzzle
asked Aug 21 '16 at 7:35
Venkat.V.S
142
Recently I got this puzzle and I was able to solve it but brute force iteration method..( trail and error iteration). I'm wondering is it possible to come-up with like a equation which on solving will give the same answers?
Puzzle:
One person had a habit of spending money according to dates.
I.e. If date is 19 he was spending Rs.19 and if date is 15, he was spending Rs. 15.One night he calculated total spending of 5 consecutive days – Monday to Friday and he found that he spent Rs. 61 in 5 days.
Ans : Feb, 27, 28 Mar 1,2,3
puzzle
asked Aug 21 '16 at 7:35
Venkat.V.S
142
edited Aug 23 '16 at 7:34
asked Aug 21 '16 at 7:35
Venkat.V.S
142
asked Aug 21 '16 at 7:35
Venkat.V.S
142
asked Aug 21 '16 at 7:35
Venkat.V.S
142
142
migrated from stats.stackexchange.com Aug 21 '16 at 9:37
This question came from our site for people interested in statistics, machine learning, data analysis, data mining, and data visualization.
migrated from stats.stackexchange.com Aug 21 '16 at 9:37
This question came from our site for people interested in statistics, machine learning, data analysis, data mining, and data visualization.
Is the answer correct? That totals to Rs. 61.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Aug 21 '16 at 9:41
Something's funky here, I can't even see the puzzle.
– Oscar Lanzi
Aug 21 '16 at 9:58
sorry the total is 61
– Venkat.V.S
Aug 23 '16 at 7:35
I tried 5x+10=61, 4x+7=61, 3x+6=61, 2x+7=61. The last one gave me the solution.
– blackpen
Aug 28 '16 at 23:30
add a comment |Â
Is the answer correct? That totals to Rs. 61.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Aug 21 '16 at 9:41
Something's funky here, I can't even see the puzzle.
– Oscar Lanzi
Aug 21 '16 at 9:58
sorry the total is 61
– Venkat.V.S
Aug 23 '16 at 7:35
I tried 5x+10=61, 4x+7=61, 3x+6=61, 2x+7=61. The last one gave me the solution.
– blackpen
Aug 28 '16 at 23:30
Is the answer correct? That totals to Rs. 61.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Aug 21 '16 at 9:41
Is the answer correct? That totals to Rs. 61.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Aug 21 '16 at 9:41
Something's funky here, I can't even see the puzzle.
– Oscar Lanzi
Aug 21 '16 at 9:58
Something's funky here, I can't even see the puzzle.
– Oscar Lanzi
Aug 21 '16 at 9:58
sorry the total is 61
– Venkat.V.S
Aug 23 '16 at 7:35
sorry the total is 61
– Venkat.V.S
Aug 23 '16 at 7:35
I tried 5x+10=61, 4x+7=61, 3x+6=61, 2x+7=61. The last one gave me the solution.
– blackpen
Aug 28 '16 at 23:30
I tried 5x+10=61, 4x+7=61, 3x+6=61, 2x+7=61. The last one gave me the solution.
– blackpen
Aug 28 '16 at 23:30
add a comment |Â
1 Answer
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0
down vote
Given that Rs.$61$ has been spent, we first note that either the days split across months, or they are all in the same month.
Suppose they are in the same month. Let us call the days as $n$, $n+1$,$n+2$, $n+3$ and $n+4$, where $n$ is the first day of spending. Then, the total of these must be $61$. This gives: $n+(n+1)+(n+2)+(n+3)+(n+4) = 61$, which simplifies to $5n=51$, and $n = 10.2$. This equation does not have a natural number solution, hence it follows that this case cannot occur.
Now, the other case must occur. However, I claim something more:
The days of spending consisit of exactly two days of the previous month and three days of the next month.
Proof: The smallest number that can be the last day of a month is $28$. Hence, the smallest possible amount of money that can be spent on the last three days of any month, is $26+27+28 = 81 > 61$. For last four or last five days, that total is even bigger, hence it follows that either the last two days or the last day of a month were included in the spending.
Suppose only one day of the previous month was part of the spending. Then, at most Rs.$31$ could have been spent on that day, and therefore the total spending is at most $31+1+2+3+4 = 41 <61$. Hence including the last day of the month was not a possibility. Hence the only option remaining is to include the last two days of the month.
Now, the first three days of the next month leads to spending of Rs.$6$. Hence, the spending of the last two days of some month is $61-6=55$. Now, suppose the last day of the month is $n$, then the amount spent in the last two days is $n+(n-1) = 2n-1$, which is equal to $55$. Hence $2n=56$, and $n=28$. Hence the previous month is a non-leap February, whose last two days are included, and the first three days of the next month, March, are to be included. Hence, the answer is Feb $27$, Feb $28$, Mar $1$, Mar $2$,Mar $3$.
answered Aug 21 '16 at 9:52
ðÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
32k22463
Doesn't that make the total as 63 (28+29+1+2+3) ? I got 27 as the answer.
– blackpen
Aug 28 '16 at 23:24
1
The question has been edited since I last wrote the answer. Now the answer is $27+28+1+2+3$.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Aug 29 '16 at 10:05
Sorry. Phew! +1.
– blackpen
Aug 29 '16 at 13:22
@blackpen Thank you it has happened to me many times as well. Now I check the history of edits before checking all the answers.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Aug 30 '16 at 8:32
Sorry, what is "n" and +3 ? Are you assuming that 2 number is on the left ie on one month (ie 27+28) and 3 numbers is on right ie on the next month. I dont want to make any assumtion. I want to come-up with an equation which will solve any similar question.. ie if the no of days and total changes.. Do you have one?
– Venkat.V.S
Aug 31 '16 at 3:29
 |Â
show 1 more comment
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Given that Rs.$61$ has been spent, we first note that either the days split across months, or they are all in the same month.
Suppose they are in the same month. Let us call the days as $n$, $n+1$,$n+2$, $n+3$ and $n+4$, where $n$ is the first day of spending. Then, the total of these must be $61$. This gives: $n+(n+1)+(n+2)+(n+3)+(n+4) = 61$, which simplifies to $5n=51$, and $n = 10.2$. This equation does not have a natural number solution, hence it follows that this case cannot occur.
Now, the other case must occur. However, I claim something more:
The days of spending consisit of exactly two days of the previous month and three days of the next month.
Proof: The smallest number that can be the last day of a month is $28$. Hence, the smallest possible amount of money that can be spent on the last three days of any month, is $26+27+28 = 81 > 61$. For last four or last five days, that total is even bigger, hence it follows that either the last two days or the last day of a month were included in the spending.
Suppose only one day of the previous month was part of the spending. Then, at most Rs.$31$ could have been spent on that day, and therefore the total spending is at most $31+1+2+3+4 = 41 <61$. Hence including the last day of the month was not a possibility. Hence the only option remaining is to include the last two days of the month.
Now, the first three days of the next month leads to spending of Rs.$6$. Hence, the spending of the last two days of some month is $61-6=55$. Now, suppose the last day of the month is $n$, then the amount spent in the last two days is $n+(n-1) = 2n-1$, which is equal to $55$. Hence $2n=56$, and $n=28$. Hence the previous month is a non-leap February, whose last two days are included, and the first three days of the next month, March, are to be included. Hence, the answer is Feb $27$, Feb $28$, Mar $1$, Mar $2$,Mar $3$.
answered Aug 21 '16 at 9:52
ðÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
32k22463
Doesn't that make the total as 63 (28+29+1+2+3) ? I got 27 as the answer.
– blackpen
Aug 28 '16 at 23:24
1
The question has been edited since I last wrote the answer. Now the answer is $27+28+1+2+3$.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Aug 29 '16 at 10:05
Sorry. Phew! +1.
– blackpen
Aug 29 '16 at 13:22
@blackpen Thank you it has happened to me many times as well. Now I check the history of edits before checking all the answers.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Aug 30 '16 at 8:32
Sorry, what is "n" and +3 ? Are you assuming that 2 number is on the left ie on one month (ie 27+28) and 3 numbers is on right ie on the next month. I dont want to make any assumtion. I want to come-up with an equation which will solve any similar question.. ie if the no of days and total changes.. Do you have one?
– Venkat.V.S
Aug 31 '16 at 3:29
 |Â
show 1 more comment
up vote
0
down vote
Given that Rs.$61$ has been spent, we first note that either the days split across months, or they are all in the same month.
Suppose they are in the same month. Let us call the days as $n$, $n+1$,$n+2$, $n+3$ and $n+4$, where $n$ is the first day of spending. Then, the total of these must be $61$. This gives: $n+(n+1)+(n+2)+(n+3)+(n+4) = 61$, which simplifies to $5n=51$, and $n = 10.2$. This equation does not have a natural number solution, hence it follows that this case cannot occur.
Now, the other case must occur. However, I claim something more:
The days of spending consisit of exactly two days of the previous month and three days of the next month.
Proof: The smallest number that can be the last day of a month is $28$. Hence, the smallest possible amount of money that can be spent on the last three days of any month, is $26+27+28 = 81 > 61$. For last four or last five days, that total is even bigger, hence it follows that either the last two days or the last day of a month were included in the spending.
Suppose only one day of the previous month was part of the spending. Then, at most Rs.$31$ could have been spent on that day, and therefore the total spending is at most $31+1+2+3+4 = 41 <61$. Hence including the last day of the month was not a possibility. Hence the only option remaining is to include the last two days of the month.
Now, the first three days of the next month leads to spending of Rs.$6$. Hence, the spending of the last two days of some month is $61-6=55$. Now, suppose the last day of the month is $n$, then the amount spent in the last two days is $n+(n-1) = 2n-1$, which is equal to $55$. Hence $2n=56$, and $n=28$. Hence the previous month is a non-leap February, whose last two days are included, and the first three days of the next month, March, are to be included. Hence, the answer is Feb $27$, Feb $28$, Mar $1$, Mar $2$,Mar $3$.
answered Aug 21 '16 at 9:52
ðÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
32k22463
Doesn't that make the total as 63 (28+29+1+2+3) ? I got 27 as the answer.
– blackpen
Aug 28 '16 at 23:24
1
The question has been edited since I last wrote the answer. Now the answer is $27+28+1+2+3$.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Aug 29 '16 at 10:05
Sorry. Phew! +1.
– blackpen
Aug 29 '16 at 13:22
@blackpen Thank you it has happened to me many times as well. Now I check the history of edits before checking all the answers.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Aug 30 '16 at 8:32
Sorry, what is "n" and +3 ? Are you assuming that 2 number is on the left ie on one month (ie 27+28) and 3 numbers is on right ie on the next month. I dont want to make any assumtion. I want to come-up with an equation which will solve any similar question.. ie if the no of days and total changes.. Do you have one?
– Venkat.V.S
Aug 31 '16 at 3:29
 |Â
show 1 more comment
up vote
0
down vote
up vote
0
down vote
Given that Rs.$61$ has been spent, we first note that either the days split across months, or they are all in the same month.
Suppose they are in the same month. Let us call the days as $n$, $n+1$,$n+2$, $n+3$ and $n+4$, where $n$ is the first day of spending. Then, the total of these must be $61$. This gives: $n+(n+1)+(n+2)+(n+3)+(n+4) = 61$, which simplifies to $5n=51$, and $n = 10.2$. This equation does not have a natural number solution, hence it follows that this case cannot occur.
Now, the other case must occur. However, I claim something more:
The days of spending consisit of exactly two days of the previous month and three days of the next month.
Proof: The smallest number that can be the last day of a month is $28$. Hence, the smallest possible amount of money that can be spent on the last three days of any month, is $26+27+28 = 81 > 61$. For last four or last five days, that total is even bigger, hence it follows that either the last two days or the last day of a month were included in the spending.
Suppose only one day of the previous month was part of the spending. Then, at most Rs.$31$ could have been spent on that day, and therefore the total spending is at most $31+1+2+3+4 = 41 <61$. Hence including the last day of the month was not a possibility. Hence the only option remaining is to include the last two days of the month.
Now, the first three days of the next month leads to spending of Rs.$6$. Hence, the spending of the last two days of some month is $61-6=55$. Now, suppose the last day of the month is $n$, then the amount spent in the last two days is $n+(n-1) = 2n-1$, which is equal to $55$. Hence $2n=56$, and $n=28$. Hence the previous month is a non-leap February, whose last two days are included, and the first three days of the next month, March, are to be included. Hence, the answer is Feb $27$, Feb $28$, Mar $1$, Mar $2$,Mar $3$.
answered Aug 21 '16 at 9:52
ðÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
32k22463
Given that Rs.$61$ has been spent, we first note that either the days split across months, or they are all in the same month.
Suppose they are in the same month. Let us call the days as $n$, $n+1$,$n+2$, $n+3$ and $n+4$, where $n$ is the first day of spending. Then, the total of these must be $61$. This gives: $n+(n+1)+(n+2)+(n+3)+(n+4) = 61$, which simplifies to $5n=51$, and $n = 10.2$. This equation does not have a natural number solution, hence it follows that this case cannot occur.
Now, the other case must occur. However, I claim something more:
The days of spending consisit of exactly two days of the previous month and three days of the next month.
Proof: The smallest number that can be the last day of a month is $28$. Hence, the smallest possible amount of money that can be spent on the last three days of any month, is $26+27+28 = 81 > 61$. For last four or last five days, that total is even bigger, hence it follows that either the last two days or the last day of a month were included in the spending.
Suppose only one day of the previous month was part of the spending. Then, at most Rs.$31$ could have been spent on that day, and therefore the total spending is at most $31+1+2+3+4 = 41 <61$. Hence including the last day of the month was not a possibility. Hence the only option remaining is to include the last two days of the month.
Now, the first three days of the next month leads to spending of Rs.$6$. Hence, the spending of the last two days of some month is $61-6=55$. Now, suppose the last day of the month is $n$, then the amount spent in the last two days is $n+(n-1) = 2n-1$, which is equal to $55$. Hence $2n=56$, and $n=28$. Hence the previous month is a non-leap February, whose last two days are included, and the first three days of the next month, March, are to be included. Hence, the answer is Feb $27$, Feb $28$, Mar $1$, Mar $2$,Mar $3$.
answered Aug 21 '16 at 9:52
ðÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
32k22463
edited Aug 31 '16 at 10:31
answered Aug 21 '16 at 9:52
ðÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
32k22463
answered Aug 21 '16 at 9:52
ðÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
32k22463
answered Aug 21 '16 at 9:52
ðÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
32k22463
32k22463
Doesn't that make the total as 63 (28+29+1+2+3) ? I got 27 as the answer.
– blackpen
Aug 28 '16 at 23:24
1
The question has been edited since I last wrote the answer. Now the answer is $27+28+1+2+3$.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Aug 29 '16 at 10:05
Sorry. Phew! +1.
– blackpen
Aug 29 '16 at 13:22
@blackpen Thank you it has happened to me many times as well. Now I check the history of edits before checking all the answers.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Aug 30 '16 at 8:32
Sorry, what is "n" and +3 ? Are you assuming that 2 number is on the left ie on one month (ie 27+28) and 3 numbers is on right ie on the next month. I dont want to make any assumtion. I want to come-up with an equation which will solve any similar question.. ie if the no of days and total changes.. Do you have one?
– Venkat.V.S
Aug 31 '16 at 3:29
 |Â
show 1 more comment
Doesn't that make the total as 63 (28+29+1+2+3) ? I got 27 as the answer.
– blackpen
Aug 28 '16 at 23:24
1
The question has been edited since I last wrote the answer. Now the answer is $27+28+1+2+3$.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Aug 29 '16 at 10:05
Sorry. Phew! +1.
– blackpen
Aug 29 '16 at 13:22
@blackpen Thank you it has happened to me many times as well. Now I check the history of edits before checking all the answers.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Aug 30 '16 at 8:32
Sorry, what is "n" and +3 ? Are you assuming that 2 number is on the left ie on one month (ie 27+28) and 3 numbers is on right ie on the next month. I dont want to make any assumtion. I want to come-up with an equation which will solve any similar question.. ie if the no of days and total changes.. Do you have one?
– Venkat.V.S
Aug 31 '16 at 3:29
Doesn't that make the total as 63 (28+29+1+2+3) ? I got 27 as the answer.
– blackpen
Aug 28 '16 at 23:24
Doesn't that make the total as 63 (28+29+1+2+3) ? I got 27 as the answer.
– blackpen
Aug 28 '16 at 23:24
1
1
The question has been edited since I last wrote the answer. Now the answer is $27+28+1+2+3$.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Aug 29 '16 at 10:05
The question has been edited since I last wrote the answer. Now the answer is $27+28+1+2+3$.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Aug 29 '16 at 10:05
Sorry. Phew! +1.
– blackpen
Aug 29 '16 at 13:22
Sorry. Phew! +1.
– blackpen
Aug 29 '16 at 13:22
@blackpen Thank you it has happened to me many times as well. Now I check the history of edits before checking all the answers.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Aug 30 '16 at 8:32
@blackpen Thank you it has happened to me many times as well. Now I check the history of edits before checking all the answers.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Aug 30 '16 at 8:32
Sorry, what is "n" and +3 ? Are you assuming that 2 number is on the left ie on one month (ie 27+28) and 3 numbers is on right ie on the next month. I dont want to make any assumtion. I want to come-up with an equation which will solve any similar question.. ie if the no of days and total changes.. Do you have one?
– Venkat.V.S
Aug 31 '16 at 3:29
Sorry, what is "n" and +3 ? Are you assuming that 2 number is on the left ie on one month (ie 27+28) and 3 numbers is on right ie on the next month. I dont want to make any assumtion. I want to come-up with an equation which will solve any similar question.. ie if the no of days and total changes.. Do you have one?
– Venkat.V.S
Aug 31 '16 at 3:29
 |Â
show 1 more comment
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Is the answer correct? That totals to Rs. 61.
– Ã°ÑÂтþý òіûûð þûþф üÑÂûûñÑÂрó
Aug 21 '16 at 9:41
Something's funky here, I can't even see the puzzle.
– Oscar Lanzi
Aug 21 '16 at 9:58
sorry the total is 61
– Venkat.V.S
Aug 23 '16 at 7:35
I tried 5x+10=61, 4x+7=61, 3x+6=61, 2x+7=61. The last one gave me the solution.
– blackpen
Aug 28 '16 at 23:30