This is a beautiful brain teaser that my wife, Pooja, asked me a few days back just before we were going to sleep – yes this was our pillow talk 🙂

Mr. Calendar spends a sum equal to the date (of that day) every day. For example, on 17th (regardless of the month), he will spend 17 Rupees, on 21st, he will spend 21 Rupees and on 7th , he will spend 7 Rupees. On 5 consecutive days, he collectively spends Rupees 63. What dates were these?

As always, please send your answers as comments within the blog (preferred), or send an e-mail to alokgoyal_2001@yahoo.com. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.

Happy Calendering!

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*Related*

Feb 28, 29, Mar 1,2 & 3

28 Feb, 29 Feb, 1 Mar, 2 Mar, 3 Mar

If the five numbers were consecutive, sum would have been a multiple of 5. Since thats not the case – we can assume that the consecutive days would have end of the month in between.

So, the dates are all from 30-x to y where x<=7, and y<=5

Since sum is 63, y=5, y=4, y=2, y=1 would not be doable (since we cannot have too few or too many large numbers)

So, y = 3

So, the dates are a, a+1, 1, 2, 3

a+a+1+1+2+3 = 63

a=28

So, the dates are 28,29,1,2,3

So its 28 Feb, 29 Feb, 1 Mar, 2 Mar, 3 Mar

28,29 in Feb and then 1,2,3 in March

28,29 of February 1,2,3 of March

Let us say the starting date is N, where N+4 < 31. So consecutive dates are N, N+1, N+2, N+3, N+4

Since (63 – SUM (1..4)) = 53 is not divisible by 5,

the solution requires the dates to wrap around at the month end.

If only one of date is towards the month end (~30), sum of other dates in next month won't add up to 63

Similarly if 3 dates are towards the end of the month, the sum will exceed 63

So 2 of the dates are towards the month end. Hence 3 dates are in the next month, i.e. 1, 2 and 3

There sum is 6. So the sum of dates in previous month is 63 – 6 = 57

Only way two numbers can add up to 57 is 28 and 29. So, the solution is

28, 29, 1, 2, 3 in a leap year Feb and Mar