+328 Mr. Prime always tell the truth when the day of the month is a prime number (i.e. the2 nd, 3rd, 5th, 7th,...), and lies on other days. Mr. Third always tell the truth on days that are multiplies of 3 (i.e. the 3rd, 6th, 9th, 12th,...), and lies on other days. On how many days in the month of January would both Mr. Prime and Mr. Third both say that they will lie the next day?
+1223 First, find the days when they will tell the truth. January has 31 days:
Prime: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31
Third: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
The dates on which they will both tell the truth are the 3rd, so there is only 1 date that works.
+37146 On how many days in the month of January would both Mr. Prime and Mr. Third both say that they will lie the next day?
Prime truth days 2 3 5 7 11 13 17 19 23 29 31
Mr prime will say that he will lie the next day the 3rd (because he is telling the truth) and the 4th
1st 3rd 4th 5th 6th 7th 10th 11th 12th 13th 16th 17th 18th 19th 22nd 23rd 28th 29th 30th 31st
Mr third
Third truth days 3 6 9 12 15 18 21 24 27 30 will say ' I will be lying tomorrow' on the following days
2nd 3rd 5th 6th 8th 9 11 12 14 15 17 18 20 21 23 24 26 27 29 30
I think ! Whew !
Common days 3 5 6 11 12 17 18 23 29 30 TEN days
