Edgar, Frank, and George are regulars at a pub. All three of them have been regulars since before this month.
1. One regular goes to the pub every two days, one goes every three days, and one goes every seven days.
2. The first day of a certain month that Edgar went to the bar was a Monday. The first day of the same month that Frank went to the bar was a Wednesday. The first day of the same month that George went to the bar was a Friday.
3. There was only one day in that month that all three men went to the pub.
On which day of that month did all three men go to the bar ?
Answer will be provided next Thursday evening after 21:00.
Teaser Of The Day No. 24
Advertisement
Re: Teaser Of The Day No. 24
ANSWER
All three men went on the 27th.
From fact 1, the first day the two-day man went to the pub was either the 1st or the 2nd of the month, and the first day the three-day man went was either the 1st, 2nd, or 3rd. But from fact 2, they could not have gone on consecutive days, so from fact 3, the two-day man must have first gone on the 1st and the three-day man must have first gone on the 3rd. This gives us two possible scenarios:
1. Edgar went to the pub on Monday the 1st and every two days thereafter, Frank went on Wednesday the 3rd and every three days thereafter, and George went on Friday the 5th and every seven days thereafter.
2. Frank went on Wednesday the 1st and every two days thereafter, George went on Friday the 3rd and every three days thereafter, and Edgar went on Monday the 6th and every seven days thereafter.
If scenario 1 is true, then Edgar went on the 1st, 3rd, 5th, 7th, 9th, 11th, 13th, 15th, 17th, 19th, 21st, 23rd, 25th, 27th, and, depending on the length of the month, the 29th and 31st, Frank went on the 3rd, 6th, 9th, 12th, 15th, 18th, 21st, 24th, 27th, and depending on the length of the month, the 30th, and George went on the 5th, 12th, 19th, and 26th. But now there was no day when all three men went to the pub. So this cannot work.
This means that scenario 2 is true. Edgar went on the 6th, 13th, 20th, and 27th. Frank went on the 1st, 3rd, 5th, 7th, 9th, 11th, 13th, 15th, 17th, 19th, 21st, 23rd, 25th, 27th, and, depending on the length of the month, the 29th and 31st. George went on the 3rd, 6th, 9th, 12th, 15th, 18th, 21st, 24th, 27th, and depending on the length of the month, the 30th. So all three men went on the 27th.
All three men went on the 27th.
From fact 1, the first day the two-day man went to the pub was either the 1st or the 2nd of the month, and the first day the three-day man went was either the 1st, 2nd, or 3rd. But from fact 2, they could not have gone on consecutive days, so from fact 3, the two-day man must have first gone on the 1st and the three-day man must have first gone on the 3rd. This gives us two possible scenarios:
1. Edgar went to the pub on Monday the 1st and every two days thereafter, Frank went on Wednesday the 3rd and every three days thereafter, and George went on Friday the 5th and every seven days thereafter.
2. Frank went on Wednesday the 1st and every two days thereafter, George went on Friday the 3rd and every three days thereafter, and Edgar went on Monday the 6th and every seven days thereafter.
If scenario 1 is true, then Edgar went on the 1st, 3rd, 5th, 7th, 9th, 11th, 13th, 15th, 17th, 19th, 21st, 23rd, 25th, 27th, and, depending on the length of the month, the 29th and 31st, Frank went on the 3rd, 6th, 9th, 12th, 15th, 18th, 21st, 24th, 27th, and depending on the length of the month, the 30th, and George went on the 5th, 12th, 19th, and 26th. But now there was no day when all three men went to the pub. So this cannot work.
This means that scenario 2 is true. Edgar went on the 6th, 13th, 20th, and 27th. Frank went on the 1st, 3rd, 5th, 7th, 9th, 11th, 13th, 15th, 17th, 19th, 21st, 23rd, 25th, 27th, and, depending on the length of the month, the 29th and 31st. George went on the 3rd, 6th, 9th, 12th, 15th, 18th, 21st, 24th, 27th, and depending on the length of the month, the 30th. So all three men went on the 27th.
¡SHARE TOPIC!