Maths Calendar Trick - Guess the dates!

You must have read in my earlier post about the calendar trick - to calculate sum of 9 numbers in 1 sec. Here is one more, you can predict the dates that your friend has selected based on their sum.

1. Ask your friend to select 4 days that form a square as shown in the adjacent figure. Let's say he has selected the 4 days as shown in the figure 5, 6, 12 and 13.

2. Ask him/her to sum up all the 4 days and tell you only the sum. Here it is 5 + 6 + 12 + 13 = 36.

Now, To guess the dates, all you need to do is to divide the sum by 4 and then subtract the result by 4. This will give the the First Date. (36/4) - 4 = 5, the reset can be calculated as below
Second Date = First Date + 1 = 5 + 1 = 6
Third Date = First Date + 7 = 5 + 7 = 12
Fourth Date = Third Date + 1 = 12 + 1 = 13

Did you understand why did it work? It is simple, say the first date is n, therefore the second is n+1, third is n+7 and fourth is n+8.
Now, by adding all the dates we have, n + (n +1) + (n + 7) + (n + 8) = 4n + 16 = 4(n + 4)
In the above example, the sum of the dates was 36. Therefore, we have
=> 4 (n + 4) = 36
=> n + 4 = 36 / 4 = 9
=> n = 9 - 4 = 5, which is nothing but the First Date.

So, now did you understand how the trick works? Let me summarize for you -
Your friend adds any 4 dates that form a square on the calendar and tells you the sum. You divide the sum by four and then subtract the result by 4 to get the first date. You add 1, 7, and 8 to get the other dates.

Have fun by trying the trick on your friends!