Mixing
Which two houses didn't get any mail that week?
Clash Royale CLAN TAG#URR8PPP
up vote
19
down vote
favorite
Postman delivers the mail in the small village. This village has
exactly ten houses, numbered from 1 to 10.
In a certain week, he did not deliver any mail at two houses in the
village but at the other houses he delivered mail three times each.
Each working day he delivered mail at exactly four houses.
The sums of the house numbers where he delivered mail were:
on Monday: 18
on Tuesday: 12
on Wednesday: 23
on Thursday: 19
on Friday: 32
on Saturday: 25
on Sunday: he never works
Which two houses didn't get any mail that week?
logical-deduction no-computers
asked Aug 28 at 11:52
rsp
1,44531026
add a comment |Â
up vote
19
down vote
favorite
Postman delivers the mail in the small village. This village has
exactly ten houses, numbered from 1 to 10.
In a certain week, he did not deliver any mail at two houses in the
village but at the other houses he delivered mail three times each.
Each working day he delivered mail at exactly four houses.
The sums of the house numbers where he delivered mail were:
on Monday: 18
on Tuesday: 12
on Wednesday: 23
on Thursday: 19
on Friday: 32
on Saturday: 25
on Sunday: he never works
Which two houses didn't get any mail that week?
logical-deduction no-computers
asked Aug 28 at 11:52
rsp
1,44531026
This puzzle would've benefited from a no-computers tag...
– ÎˆÃÂικ ΚÉνÃÄανÄÃŒÀοÅλοÂ
Aug 28 at 12:21
Not recommended to change the tags now that an answer has been accepted. I was just underway making a program to calculate this, integer partitions. :P
– ÎˆÃÂικ ΚÉνÃÄανÄÃŒÀοÅλοÂ
Aug 28 at 12:30
3
@ΈÃÂικΚÉνÃÄανÄÃŒÀοÅλο The tag is welcome. Even if an answer was accepted, it's still interesting to know that this puzzle was "designed to be solved without using calculators or computer programming".
– xhienne
Aug 28 at 12:36
add a comment |Â
up vote
19
down vote
favorite
up vote
19
down vote
favorite
Postman delivers the mail in the small village. This village has
exactly ten houses, numbered from 1 to 10.
In a certain week, he did not deliver any mail at two houses in the
village but at the other houses he delivered mail three times each.
Each working day he delivered mail at exactly four houses.
The sums of the house numbers where he delivered mail were:
on Monday: 18
on Tuesday: 12
on Wednesday: 23
on Thursday: 19
on Friday: 32
on Saturday: 25
on Sunday: he never works
Which two houses didn't get any mail that week?
logical-deduction no-computers
asked Aug 28 at 11:52
rsp
1,44531026
Postman delivers the mail in the small village. This village has
exactly ten houses, numbered from 1 to 10.
In a certain week, he did not deliver any mail at two houses in the
village but at the other houses he delivered mail three times each.
Each working day he delivered mail at exactly four houses.
The sums of the house numbers where he delivered mail were:
on Monday: 18
on Tuesday: 12
on Wednesday: 23
on Thursday: 19
on Friday: 32
on Saturday: 25
on Sunday: he never works
Which two houses didn't get any mail that week?
logical-deduction no-computers
asked Aug 28 at 11:52
rsp
1,44531026
edited Aug 28 at 12:24
asked Aug 28 at 11:52
rsp
1,44531026
asked Aug 28 at 11:52
rsp
1,44531026
asked Aug 28 at 11:52
rsp
1,44531026
1,44531026
This puzzle would've benefited from a no-computers tag...
– ÎˆÃÂικ ΚÉνÃÄανÄÃŒÀοÅλοÂ
Aug 28 at 12:21
Not recommended to change the tags now that an answer has been accepted. I was just underway making a program to calculate this, integer partitions. :P
– ÎˆÃÂικ ΚÉνÃÄανÄÃŒÀοÅλοÂ
Aug 28 at 12:30
3
@ΈÃÂικΚÉνÃÄανÄÃŒÀοÅλο The tag is welcome. Even if an answer was accepted, it's still interesting to know that this puzzle was "designed to be solved without using calculators or computer programming".
– xhienne
Aug 28 at 12:36
add a comment |Â
This puzzle would've benefited from a no-computers tag...
– ÎˆÃÂικ ΚÉνÃÄανÄÃŒÀοÅλοÂ
Aug 28 at 12:21
Not recommended to change the tags now that an answer has been accepted. I was just underway making a program to calculate this, integer partitions. :P
– ÎˆÃÂικ ΚÉνÃÄανÄÃŒÀοÅλοÂ
Aug 28 at 12:30
3
@ΈÃÂικΚÉνÃÄανÄÃŒÀοÅλο The tag is welcome. Even if an answer was accepted, it's still interesting to know that this puzzle was "designed to be solved without using calculators or computer programming".
– xhienne
Aug 28 at 12:36
This puzzle would've benefited from a no-computers tag...
– ÎˆÃÂικ ΚÉνÃÄανÄÃŒÀοÅλοÂ
Aug 28 at 12:21
This puzzle would've benefited from a no-computers tag...
– ÎˆÃÂικ ΚÉνÃÄανÄÃŒÀοÅλοÂ
Aug 28 at 12:21
Not recommended to change the tags now that an answer has been accepted. I was just underway making a program to calculate this, integer partitions. :P
– ÎˆÃÂικ ΚÉνÃÄανÄÃŒÀοÅλοÂ
Aug 28 at 12:30
Not recommended to change the tags now that an answer has been accepted. I was just underway making a program to calculate this, integer partitions. :P
– ÎˆÃÂικ ΚÉνÃÄανÄÃŒÀοÅλοÂ
Aug 28 at 12:30
3
3
@ΈÃÂικΚÉνÃÄανÄÃŒÀοÅλο The tag is welcome. Even if an answer was accepted, it's still interesting to know that this puzzle was "designed to be solved without using calculators or computer programming".
– xhienne
Aug 28 at 12:36
@ΈÃÂικΚÉνÃÄανÄÃŒÀοÅλο The tag is welcome. Even if an answer was accepted, it's still interesting to know that this puzzle was "designed to be solved without using calculators or computer programming".
– xhienne
Aug 28 at 12:36
add a comment |Â
3 Answers
3
active
oldest
votes
up vote
20
down vote
accepted
I think the house numbers which don't get mail are
$4$ and $8$
Reasoning
Given the premise of the problem, the sum of the numbers over the whole week should be equal to three times the sum of the numbers of the houses that get mail, that is
$ 18 + 12 + 23 + 19 + 32 + 25 = 129 = 3 times 43$ (Thank you, Marius!)
And so the sum of the numbers of the houses which don't get mail is $55 - 43 = 12$.
Hence, the only possibilities for houses which don't get mail are the pairs $(5,7)$, $(4,8)$, $(3,9)$ and $(2,10)$.
Given that on Friday, the sum of the four houses that get mail is $32$, which is greater than $9 + 8 + 7 + 6$ and $10 + 8 + 7 + 6$, this means that both houses $9$ and $10$ must receive mail.
Also $32$ cannot be made with four houses without using either $5$ or $7$ (since $10+9+8+6 > 32$ and $10+9+8+4 < 32$) so the only remaining possibility is $(4,8)$ for the houses that don't get mail.
answered Aug 28 at 12:03
hexomino
28.9k292144
3
love the reasoning, but you should use a calculator next time...do the math again :) specially when dividing something by 3 (or multiplying...depends on how you see it)
– Marius
Aug 28 at 12:04
@Marius Thank you, completely missed that.
– hexomino
Aug 28 at 12:08
You're welcome. Just noticed because I started on the same approach and got a different sum
– Marius
Aug 28 at 12:08
1
@rsp Yes, thanks to a little help.
– hexomino
Aug 28 at 12:12
1
I was too slow on this one. I went for the small numbers instead and used Tuesday's 12 to eliminate most options but was still stuck on the last two possibilities when I saw your answer.
– Jaap Scherphuis
Aug 28 at 12:18
add a comment |Â
up vote
2
down vote
Tuesday's delivery would have been 1+2+3+6 or 1+2+4+5. Friday's delivery would have been 5+8+9+10 or 6+7+9+10. This means the solution is a pair picked from one of the 4 combinations 4+7, 4+5+8, 3+6+7, 3+8.
The total delivered house numbers were 129. Had every house gotten 3 deliveries, it would have been 55*3=165, so the sum of the missing numbers is (165-129)/3 = 12. Only 4+8 fits the bill.
add a comment |Â
up vote
1
down vote
10, 9,7,6, 5,3,2,1 get mail, and 8 and 4 dont.
10 and 9 should be in the 32 combined with either 8 and 5 or 7 and 6.
The total sum is 129, knowing that 57 (for 10 and 9) and 39 (either 8
and 5 or 7 and 6) could be substracted. Leaving 33 which is relative
low, so i calculated (1 +2 +3 +4 ) *3 =30, and followed that the 4
needs to be replaced by the 5.
answered Aug 28 at 13:56
chris
111
add a comment |Â
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
20
down vote
accepted
I think the house numbers which don't get mail are
$4$ and $8$
Reasoning
Given the premise of the problem, the sum of the numbers over the whole week should be equal to three times the sum of the numbers of the houses that get mail, that is
$ 18 + 12 + 23 + 19 + 32 + 25 = 129 = 3 times 43$ (Thank you, Marius!)
And so the sum of the numbers of the houses which don't get mail is $55 - 43 = 12$.
Hence, the only possibilities for houses which don't get mail are the pairs $(5,7)$, $(4,8)$, $(3,9)$ and $(2,10)$.
Given that on Friday, the sum of the four houses that get mail is $32$, which is greater than $9 + 8 + 7 + 6$ and $10 + 8 + 7 + 6$, this means that both houses $9$ and $10$ must receive mail.
Also $32$ cannot be made with four houses without using either $5$ or $7$ (since $10+9+8+6 > 32$ and $10+9+8+4 < 32$) so the only remaining possibility is $(4,8)$ for the houses that don't get mail.
answered Aug 28 at 12:03
hexomino
28.9k292144
3
love the reasoning, but you should use a calculator next time...do the math again :) specially when dividing something by 3 (or multiplying...depends on how you see it)
– Marius
Aug 28 at 12:04
@Marius Thank you, completely missed that.
– hexomino
Aug 28 at 12:08
You're welcome. Just noticed because I started on the same approach and got a different sum
– Marius
Aug 28 at 12:08
1
@rsp Yes, thanks to a little help.
– hexomino
Aug 28 at 12:12
1
I was too slow on this one. I went for the small numbers instead and used Tuesday's 12 to eliminate most options but was still stuck on the last two possibilities when I saw your answer.
– Jaap Scherphuis
Aug 28 at 12:18
add a comment |Â
up vote
20
down vote
accepted
I think the house numbers which don't get mail are
$4$ and $8$
Reasoning
Given the premise of the problem, the sum of the numbers over the whole week should be equal to three times the sum of the numbers of the houses that get mail, that is
$ 18 + 12 + 23 + 19 + 32 + 25 = 129 = 3 times 43$ (Thank you, Marius!)
And so the sum of the numbers of the houses which don't get mail is $55 - 43 = 12$.
Hence, the only possibilities for houses which don't get mail are the pairs $(5,7)$, $(4,8)$, $(3,9)$ and $(2,10)$.
Given that on Friday, the sum of the four houses that get mail is $32$, which is greater than $9 + 8 + 7 + 6$ and $10 + 8 + 7 + 6$, this means that both houses $9$ and $10$ must receive mail.
Also $32$ cannot be made with four houses without using either $5$ or $7$ (since $10+9+8+6 > 32$ and $10+9+8+4 < 32$) so the only remaining possibility is $(4,8)$ for the houses that don't get mail.
answered Aug 28 at 12:03
hexomino
28.9k292144
3
love the reasoning, but you should use a calculator next time...do the math again :) specially when dividing something by 3 (or multiplying...depends on how you see it)
– Marius
Aug 28 at 12:04
@Marius Thank you, completely missed that.
– hexomino
Aug 28 at 12:08
You're welcome. Just noticed because I started on the same approach and got a different sum
– Marius
Aug 28 at 12:08
1
@rsp Yes, thanks to a little help.
– hexomino
Aug 28 at 12:12
1
I was too slow on this one. I went for the small numbers instead and used Tuesday's 12 to eliminate most options but was still stuck on the last two possibilities when I saw your answer.
– Jaap Scherphuis
Aug 28 at 12:18
add a comment |Â
up vote
20
down vote
accepted
up vote
20
down vote
accepted
I think the house numbers which don't get mail are
$4$ and $8$
Reasoning
Given the premise of the problem, the sum of the numbers over the whole week should be equal to three times the sum of the numbers of the houses that get mail, that is
$ 18 + 12 + 23 + 19 + 32 + 25 = 129 = 3 times 43$ (Thank you, Marius!)
And so the sum of the numbers of the houses which don't get mail is $55 - 43 = 12$.
Hence, the only possibilities for houses which don't get mail are the pairs $(5,7)$, $(4,8)$, $(3,9)$ and $(2,10)$.
Given that on Friday, the sum of the four houses that get mail is $32$, which is greater than $9 + 8 + 7 + 6$ and $10 + 8 + 7 + 6$, this means that both houses $9$ and $10$ must receive mail.
Also $32$ cannot be made with four houses without using either $5$ or $7$ (since $10+9+8+6 > 32$ and $10+9+8+4 < 32$) so the only remaining possibility is $(4,8)$ for the houses that don't get mail.
answered Aug 28 at 12:03
hexomino
28.9k292144
I think the house numbers which don't get mail are
$4$ and $8$
Reasoning
Given the premise of the problem, the sum of the numbers over the whole week should be equal to three times the sum of the numbers of the houses that get mail, that is
$ 18 + 12 + 23 + 19 + 32 + 25 = 129 = 3 times 43$ (Thank you, Marius!)
And so the sum of the numbers of the houses which don't get mail is $55 - 43 = 12$.
Hence, the only possibilities for houses which don't get mail are the pairs $(5,7)$, $(4,8)$, $(3,9)$ and $(2,10)$.
Given that on Friday, the sum of the four houses that get mail is $32$, which is greater than $9 + 8 + 7 + 6$ and $10 + 8 + 7 + 6$, this means that both houses $9$ and $10$ must receive mail.
Also $32$ cannot be made with four houses without using either $5$ or $7$ (since $10+9+8+6 > 32$ and $10+9+8+4 < 32$) so the only remaining possibility is $(4,8)$ for the houses that don't get mail.
answered Aug 28 at 12:03
hexomino
28.9k292144
edited Aug 28 at 12:14
answered Aug 28 at 12:03
hexomino
28.9k292144
answered Aug 28 at 12:03
hexomino
28.9k292144
answered Aug 28 at 12:03
hexomino
28.9k292144
28.9k292144
3
love the reasoning, but you should use a calculator next time...do the math again :) specially when dividing something by 3 (or multiplying...depends on how you see it)
– Marius
Aug 28 at 12:04
@Marius Thank you, completely missed that.
– hexomino
Aug 28 at 12:08
You're welcome. Just noticed because I started on the same approach and got a different sum
– Marius
Aug 28 at 12:08
1
@rsp Yes, thanks to a little help.
– hexomino
Aug 28 at 12:12
1
I was too slow on this one. I went for the small numbers instead and used Tuesday's 12 to eliminate most options but was still stuck on the last two possibilities when I saw your answer.
– Jaap Scherphuis
Aug 28 at 12:18
add a comment |Â
3
love the reasoning, but you should use a calculator next time...do the math again :) specially when dividing something by 3 (or multiplying...depends on how you see it)
– Marius
Aug 28 at 12:04
@Marius Thank you, completely missed that.
– hexomino
Aug 28 at 12:08
You're welcome. Just noticed because I started on the same approach and got a different sum
– Marius
Aug 28 at 12:08
1
@rsp Yes, thanks to a little help.
– hexomino
Aug 28 at 12:12
1
I was too slow on this one. I went for the small numbers instead and used Tuesday's 12 to eliminate most options but was still stuck on the last two possibilities when I saw your answer.
– Jaap Scherphuis
Aug 28 at 12:18
3
3
love the reasoning, but you should use a calculator next time...do the math again :) specially when dividing something by 3 (or multiplying...depends on how you see it)
– Marius
Aug 28 at 12:04
love the reasoning, but you should use a calculator next time...do the math again :) specially when dividing something by 3 (or multiplying...depends on how you see it)
– Marius
Aug 28 at 12:04
@Marius Thank you, completely missed that.
– hexomino
Aug 28 at 12:08
@Marius Thank you, completely missed that.
– hexomino
Aug 28 at 12:08
You're welcome. Just noticed because I started on the same approach and got a different sum
– Marius
Aug 28 at 12:08
You're welcome. Just noticed because I started on the same approach and got a different sum
– Marius
Aug 28 at 12:08
1
1
@rsp Yes, thanks to a little help.
– hexomino
Aug 28 at 12:12
@rsp Yes, thanks to a little help.
– hexomino
Aug 28 at 12:12
1
1
I was too slow on this one. I went for the small numbers instead and used Tuesday's 12 to eliminate most options but was still stuck on the last two possibilities when I saw your answer.
– Jaap Scherphuis
Aug 28 at 12:18
I was too slow on this one. I went for the small numbers instead and used Tuesday's 12 to eliminate most options but was still stuck on the last two possibilities when I saw your answer.
– Jaap Scherphuis
Aug 28 at 12:18
add a comment |Â
up vote
2
down vote
Tuesday's delivery would have been 1+2+3+6 or 1+2+4+5. Friday's delivery would have been 5+8+9+10 or 6+7+9+10. This means the solution is a pair picked from one of the 4 combinations 4+7, 4+5+8, 3+6+7, 3+8.
The total delivered house numbers were 129. Had every house gotten 3 deliveries, it would have been 55*3=165, so the sum of the missing numbers is (165-129)/3 = 12. Only 4+8 fits the bill.
add a comment |Â
up vote
2
down vote
Tuesday's delivery would have been 1+2+3+6 or 1+2+4+5. Friday's delivery would have been 5+8+9+10 or 6+7+9+10. This means the solution is a pair picked from one of the 4 combinations 4+7, 4+5+8, 3+6+7, 3+8.
The total delivered house numbers were 129. Had every house gotten 3 deliveries, it would have been 55*3=165, so the sum of the missing numbers is (165-129)/3 = 12. Only 4+8 fits the bill.
add a comment |Â
up vote
2
down vote
up vote
2
down vote
Tuesday's delivery would have been 1+2+3+6 or 1+2+4+5. Friday's delivery would have been 5+8+9+10 or 6+7+9+10. This means the solution is a pair picked from one of the 4 combinations 4+7, 4+5+8, 3+6+7, 3+8.
The total delivered house numbers were 129. Had every house gotten 3 deliveries, it would have been 55*3=165, so the sum of the missing numbers is (165-129)/3 = 12. Only 4+8 fits the bill.
Tuesday's delivery would have been 1+2+3+6 or 1+2+4+5. Friday's delivery would have been 5+8+9+10 or 6+7+9+10. This means the solution is a pair picked from one of the 4 combinations 4+7, 4+5+8, 3+6+7, 3+8.
The total delivered house numbers were 129. Had every house gotten 3 deliveries, it would have been 55*3=165, so the sum of the missing numbers is (165-129)/3 = 12. Only 4+8 fits the bill.
answered Aug 28 at 13:52
user51917
add a comment |Â
add a comment |Â
up vote
1
down vote
10, 9,7,6, 5,3,2,1 get mail, and 8 and 4 dont.
10 and 9 should be in the 32 combined with either 8 and 5 or 7 and 6.
The total sum is 129, knowing that 57 (for 10 and 9) and 39 (either 8
and 5 or 7 and 6) could be substracted. Leaving 33 which is relative
low, so i calculated (1 +2 +3 +4 ) *3 =30, and followed that the 4
needs to be replaced by the 5.
answered Aug 28 at 13:56
chris
111
add a comment |Â
up vote
1
down vote
10, 9,7,6, 5,3,2,1 get mail, and 8 and 4 dont.
10 and 9 should be in the 32 combined with either 8 and 5 or 7 and 6.
The total sum is 129, knowing that 57 (for 10 and 9) and 39 (either 8
and 5 or 7 and 6) could be substracted. Leaving 33 which is relative
low, so i calculated (1 +2 +3 +4 ) *3 =30, and followed that the 4
needs to be replaced by the 5.
answered Aug 28 at 13:56
chris
111
add a comment |Â
up vote
1
down vote
up vote
1
down vote
10, 9,7,6, 5,3,2,1 get mail, and 8 and 4 dont.
10 and 9 should be in the 32 combined with either 8 and 5 or 7 and 6.
The total sum is 129, knowing that 57 (for 10 and 9) and 39 (either 8
and 5 or 7 and 6) could be substracted. Leaving 33 which is relative
low, so i calculated (1 +2 +3 +4 ) *3 =30, and followed that the 4
needs to be replaced by the 5.
answered Aug 28 at 13:56
chris
111
10, 9,7,6, 5,3,2,1 get mail, and 8 and 4 dont.
10 and 9 should be in the 32 combined with either 8 and 5 or 7 and 6.
The total sum is 129, knowing that 57 (for 10 and 9) and 39 (either 8
and 5 or 7 and 6) could be substracted. Leaving 33 which is relative
low, so i calculated (1 +2 +3 +4 ) *3 =30, and followed that the 4
needs to be replaced by the 5.
answered Aug 28 at 13:56
chris
111
answered Aug 28 at 13:56
chris
111
answered Aug 28 at 13:56
chris
111
answered Aug 28 at 13:56
chris
111
111
add a comment |Â
add a comment |Â
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This puzzle would've benefited from a no-computers tag...
– ÎˆÃÂικ ΚÉνÃÄανÄÃŒÀοÅλοÂ
Aug 28 at 12:21
Not recommended to change the tags now that an answer has been accepted. I was just underway making a program to calculate this, integer partitions. :P
– ÎˆÃÂικ ΚÉνÃÄανÄÃŒÀοÅλοÂ
Aug 28 at 12:30
3
@ΈÃÂικΚÉνÃÄανÄÃŒÀοÅλο The tag is welcome. Even if an answer was accepted, it's still interesting to know that this puzzle was "designed to be solved without using calculators or computer programming".
– xhienne
Aug 28 at 12:36