I have a puzzle which I think everyone is capable of doing, though it takes some thinking.
Let's say that the day number d of any date is a number from 0 to 6, with SUN = 0, MON = 1, TUE = 2, WED = 3, THU = 4, FRI = 5, SAT = 6.
EXAMPLES: the day number of WED 16 SEP 2015 is 3 because it's a Wednesday, and the day number of THU 17 SEP 2015 is 4 because it's a Thursday.
PUZZLE: If you are given the day number d of 01 January of any year, how many days must you add to that first day to get to the first Monday of that year? For example, the first day of this year THU 01 JAN 2015, so you would have to add on 4 days to get to the first Monday. For this puzzle, however, you have to provide a formula (such as 2 x d + 1) for ANY year.
You can use add +, subtract -, multiply ×, and brackets.
You can also use divide ÷, but assume this always gives the whole number only, so:
10 ÷ 2 = 5 20 ÷ 4 = 5 23 ÷ 10 = 2
11 ÷ 2 = 5 21 ÷ 4 = 5 35 ÷ 10 = 3
12 ÷ 2 = 6 25 ÷ 4 = 6 48 ÷ 10 = 4
13 ÷ 2 = 6 27 ÷ 4 = 6 89 ÷ 10 = 8
You can also use remainder %, which always gives the remainder of a divide (which I hope you remember from primary school), so:
10 % 2 = 0 20 % 4 = 0 23 % 10 = 3
11 % 2 = 1 21 % 4 = 1 35 % 10 = 5
12 % 2 = 0 25 % 4 = 1 48 % 10 = 8
13 % 2 = 1 27 % 4 = 3 89 % 10 = 9
So your answer might look like this: You have to add on (d % 10) ÷ 2 days to get to the first Monday of the year, where d is the day number of 1 JAN of that year. (And, no, this is not the correct answer, before everyone on the board PMs me this.)
The first person who provides the correct answer gets a GENIUS badge.
Feel free to post here, but PM the answer once you have it.
Those who find this easy might wish to come up with a second formula for the number of days you have to subtract from the last day of the year (31 DEC) to get the last Monday of the year, again assuming you know the day number of the last day of the year.
