# The weird meeting riddle

There are twelve friends: Edward, Steve, Oscar, Amelie, Alexander, Cayson, Bradley, Gabriel, Kamila, Allen, Luis and Connor. We know that:

• Edward works on odd Fridays
• Steve works on non-square days
• Oscar works on multiples of 3 or 4
• Amelie works on days which contain the digit 1 and are not working Tuesdays for Oscar
• Alexander works on prime Tuesdays
• Cayson works on even days, except for Sundyas
• Bradley works on two-digit days
• Gabriel works on composite days, except for Fridays
• Kamila works on two-digit Saturdays having different digits
• Allen works during the week and on composite Saturdays
• Louis always works, except for odd Tuesdays
• Connor works on days which are not multiples of 5 as well as on Thursdays.

On Thursday, August 23, they decide to arrange a meeting which will be held in either September or October. The date of the meeting must meet the following conditions:

• at least 6 people have to participate
• the meeting won't be held on a Wednesday
• the meeting won't be held on an odd Monday
• the meeting won't be held on a prime Friday
• the meeting won't be held on the 30th
• the digit 2 does not appear in the day
• the day of the meeting is not a square
• Amelie wants to participate.

When will the meeting be?

## Hint

Hint
The information Thursday, August 23 is the key to the problem. You can solve it by writing down, for each day of September, who's free on that day and then doing the same for October.

## Solution

Solution
After writing down, for each day, who doesn't work on that day, we have to figure out when the meeting will take place.

The first condition says that at least 6 people are required to join in. That means that September 6 gets canceled, because only 5 people are free on that day. For the same reason, the days 8 and 10 are excluded too. Other days which are excluded are 12, 14, 15, 18, 20, 21, 22, 24, 26, 27 and 28. In October, the days which are excluded are 6, 8, 10, 12, 15, 16, 18, 19, 20, 21, 22, 24, 27 and 30.
The second condition says that the meeting will not be held on a Wednesday, which means that from September, the days 5 and 19 are excluded, while from October, the days 3, 17 and 31 are canceled.
The third condition says that the date of the meeting is not an odd Monday. So from September we exclude the days 3 and 17, while from October we exclude the days 1 and 29.
The fourth condition says that it’s not a prime Friday. So from September we cancel the day 7, while from October we cancel the day 5 (26 is left for now because it’s a composite number).
The fifth condition says the meeting will not be on the 30th of either month. We have already excluded it from October, now we will exclude it from September as well.
The sixth condition says the meeting won’t be held on a day which has the digit 2 in it, so we have to exclude the days 2, 23, 25 and 29 from September and 2, 23, 25, 26, 28 from October.
The seventh condition says the day of the meeting is not a square. So we exclude the days 1, 4, 9 and 16 from September and 4 and 9 from October.
Now, the final condition: Amelie wants to take part in the meeting. These are the days that we left: September 11, September 13, October 7, October 11, October 13, October 14. We know that Amelie works on days which have the digit 1 in them and are not working Tuesdays for Oscar. The only Tuesday that we have is September 11, but Oscar doesn’t work on that day (it’s not a multiple of either 3 or 4), so Amelie does. And the only day in the list when Amelie is free is October 7, which is the solution of the riddle.

If this method seems too long, you can start right from the conditions. Then the days 5, 12, 19 and 26 are canceled from September and the days 3, 10, 17, 24 and 31 are canceled from October, because they're all Wednesdays; from September, the days 3 and 17 and from October, the days 1, 15 and 29 are canceled, because they're all odd Mondays; September 7 and October 5 are removed, because they're prime Fridays; the day 30 is removed from both months; all the days which have the digit 2 in them (2, 20, 21, 22, 23, 24, 25, 27, 28, 29 for September and 2, 12, 20, 21, 22, 23, 25, 26, 27, 28 for October) are canceled and finally, from September, the days 1, 4, 9 and 16 and from October, the days 4, 9 and 16 are canceled, because they're all squares. The remaining days are, for September: 6, 8, 10, 11, 13, 14, 15 and 18 and for October: 6, 7, 8, 11, 13, 14, 18 and 19. But from September, the days 6, 8, 10, 14, 15 and 18 are removed, and so are the days 6, 8, 18 and 19 from October, because none of them meets the first condition (which says that at least 6 people are required). Among the remaining days, the only one when Amelie is free is October 7.