Paul the postal carrier had an unusual week involving the ten properties along Park Place. Each day of the week Monday through Saturday he delivered mail to four houses. Eight of the houses received mail on three days and two houses got no mail.
The houses along Park Place are numbered 1 to 10. The sum of the house numbers Paul delivered for each day of the week were:
- Monday: 12
- Tuesday: 18
- Wednesday: 23
- Thursday: 32
- Friday: 25
- Saturday: 19
Which two houses did not receive mail?
the total of house numbers on all six days comes to 129.
as the postman delivers to 4 houses for 6 days he serves 24 mails.
So, each of the 8 delivered houses has got 3 mails each.
129=3(sum of the eight house numbers)
so sum of houses recieving mail is 43. total for 1 to 10 is 55. So the sum of house numbers of the two houses that dont get mail has to be 12. this gives four possibilities (10,2); (9,3); (8,4); (7,5)
if number 10 has not got any mail then maximum total for a day becomes 9+8+7+6= 30. But on thursday it is 32 so 10 has got mail which eliminates (10,2)
Similarly if 9 has got no mail then max possible is 10+8+7+6= 31. which is also not possible. so (9,3) also eliminated.
Finally, if 7 gets no mail then 32 can be made only by 10+9+8+5 but this requires a 5. So one of 7 and 5 has to be delivered to which excludes the possibility of (7,5) being a solution.
Hence 4 and 8 are the house numbers to which no mail is delivered.
Logic Solution - no computer etc.
