“If one stacked 73 dice on top of each other on a table, what would be the sum of the numbers that are covered if the top die shows a 3?”

-Park Math, Book 1, p11

I can imagine handing out dice and asking kids to stack them with various numbers on top. We could ask for sums, and then eventually formulas or equations, depending on what stage in the game we’re at.

**Extensions**

- Is the sum of the covered stuff ever equal to the sum of the uncovered stuff? Why or why not?
- What’s the sum of the dice in this thing? (John Burk)
- What if it’s an 8 sided die? 20 sided die?
- If you’ve minimized the product of the covered numbers, what’s the sum?
- The sum of the covered numbers in a stack of dice is 25. What are the min and max products of the covered numbers? (Justin Lanier)
- Can you get any number as the sum?

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*Related*

In a die, when you add the opposite sides, it always sums to 7, knowing that out of 73 dice, 72 dice are covered both the sides and the 73rd is covered only one side by leaving the top showing 4. so the the other side of the 73rd die is 3.

So the sum of numbers covered is = (72*7)+3 => 507.

From,

Sathya Niharika

Chennai