# Sunday Times Teaser 2788 – Red-Letter Days

*by Nick MacKinnon*

#### Published: 28 February 2016 (link)

The months of my 2016 calendar are headed M, T, W, Th, F, Sa, Su, with the dates 1, 2, 3 … in a grid of squares underneath. I have shaded all the days on which I have meetings planned — all of them being on weekdays. For example, in February the days 1, 2, 3, 4, 8 and 9 are shaded: these shaded squares form a connected piece and the product of the numbers is a perfect cube. The same is true of the shaded squares in another month — and in fact it’s the largest possible such cube in the calendar. My last meeting in that month is on my aunt’s birthday.

What is her birthday?

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I liked this teaser but it is one that is a great deal less effort when done manually rather than by computer. Fortunately, however, I had various pieces already (finding connected areas in a grid of cells was needed in Teaser 2773) so it was not too hard to put a program together.

Brian, would I be right in thinking your program finds a maximum connected region of 12^3 for August?

Because I think you can get to 120^3 using [1, 2, 3, 4, 5, 8, 10, 12, 15].

It also works for February. Other than that the maximum values my program finds agree with yours.

Hi Jim,

Yes, it misses the 120^3 because I wrongly excluded day 1 from the grid. I have changed it now because that is not the only issue with my original version, which might have missed a maximum cube because I didn’t check all combinations of days, only the most likely ones.