My first thought was that heaps begin when you have 3 or more layers in every direction so a layer of 9 with a layer of 4 on top and a single grain to top of the pyramid. So heaps begin at 14 grains if suitably arranged.
Which lead to my second thought that a million grains are not a heap if they are laid out in a line so the arrangement is key to the heap-iness. Indeed take the heap in the picture (which I hope we can all agree is a fine exemplar of a heap), and form it in to a perfect cube and is it still a heap ? I think not ( three thoughts on the trot, I need a lie down) . So an element of randomness as well as a minimum size is required for a true heap. How to quantify the randomness required is left for the reader (if there still are any!)
I started off thinking it should be 3 and 4 cubits, but then realized I had to double it. My brain likes to work with whole numbers as a starting point, so I was looking for multiples of 3 and 4.
Or - it is the Richard Feynman problem solving algorithm - 1. write down the problem, 2. think very hard, 3. write down the answer!
Regarding heaps, they need to be bigger at the bottom than at the top, presumably due to gravity. I think heaps can be less than 14 if the individual elements are not regular. Even if they are regular I think you could have a heap of, for example,12 bricks.
The numbers you see are laid out according to a specific rule.
Once you have figured out this rule, you should be able to replace the “?” with the correct numbers.
I assure you that the number at the bottom is definitely 7. It is not a typo.
And as a result, the “?” is not 15.
Now, as encouragement, when I first encountered this teaser, I also felt that the bottom number should be 8. And boy-oh-boy did it take some effort to discard the “99 - 72 = 27” syndrome that had accumulated in my head. I just couldn’t look at those numbers any other way. You all did incredibly well to spot the 99 - 72 = 27 pattern. And to realise there might be typo !
Hint: Just remember, we live in a “digital” age (but you won’t need a calculator or a computer). And this is a “Brain Teaser” thread ie a bit of lateral thinking is sometimes needed !
Sorry Ian, the “digital” hint was meant to direct people towards the individual digits…and the “lateral” hint was intended to set a focus on the four lateral digits that create the next number in sequence… but you know that now ! Nonetheless, i’m sure you’re now up to full speed with binary and hex numbers again
