The functions log_2 and 2^x are clearly linked to TT. How many bits would you need to use to build a counter up to N? (log_2 N). How high can you count with these N bits? (2^N). So, asking what is the largest number that they can count up to and stop (if they have enough parts) could be a good exercise. Some kids might try to build it. Or, you could just reason it out based on the number of bits you have available, and the height of the board, whichever is smaller, and take into consideration the space needed for an interceptor.

Perhaps you could get them to solve some simple linear equations. Implement the function 4*n, where n is set in a column of bits. Cover up the counter to 4 (which is used to multiply) with a piece of paper taped over it loosely, then have them set the n bits to a value (say 7) and observe the output (28). From this, they need to write the equation 7x=28, where x is representing what is hidden. When they take off the cover, surprise… there are two bit pieces, so x is 4.

Here’s a question: using multiplication, what is the largest value they can multiply up to using a stack of x bits and a stack of y bits?

Another: if I give you n bit pieces, using multiplication of a stack of x bits and a stack of n-x bits, what is the largest value you can multiply up to? (2^x times 2^(n-x) will always be 2^n, so it shouldn’t matter - a nice surprise!) To discover this, give them, say, 8 bit pieces, and have different kids build an x times y counter, where x+y=8, for different values of x and y. Ask them to see how high it counts (multiplies). They should all get the same answer. Why? (Again, 2^x times 2^y = 2^8 in every case.

That’s all I got for now.