Six sheets are set out in a room. Each identifies a different date in the same month. Weekdays (Monday to Saturday) are printed in black and Sundays in red. Six people will enter the room, one by one. Before the first one enters, one sheet is turned face down. Candidate 1 is then asked if she can deduce the color of the inverted sheet by examining the other sheets. Her answer, yes or no, is written on the back of the inverted sheet, followed by her number, 1.
When 1 departs, a second sheet is turned face down. Candidate 2 enters and is asked whether she can deduce the color of the second sheet by considering her predecessor’s answer and the four face-up sheets.
Her answer is noted in its turn, and this process continues — when the sixth candidate enters, she sees six face-down sheets, the first five of which bear the answers of the first five candidates.
If all five of these answers are no, can Candidate 6 answer yes and be right?

Source: Roland Sprague, Recreation in Mathematics, 1963

Candidate 1 can only deduce the color on sheet one if she sees all the Sundays for that month on the other five sheets. (Could be 4 numbers if the Sundays are like 6,13,20,27 or 5 numbers if the Sundays are like 2,9,16,23,30.)

Posted by Brian Smith on 2018-12-25 23:03:30