You work at a basketball stadium and you can expect a maximum of 6000 people to come in for a busy
event. The tally counter in the picture has 4 wheels each with 10 digits, so it should work out for you
since it can count from 0000 to 9999.
Since each wheel has 10 digits, the Tally Counter Manufacturer (TCM) charges $10 per wheel. The
tally counter in the picture would cost $40 because it has 4 wheels each with 10 digits.
TCM also makes wheels for their tally counters of sizes (2,3,4,5,6,7,8,9) and charges $n per wheel with
n digits. For example, you could by a tally counter where each wheel has only 5 digits (0,1,2,3,4) and
each one of these wheels would cost $5. Since you know how to read integers in any base, you decide
to explore your options.
(a) Compute the prices of tally counters with at least 6000 capacity using wheels of sizes:

2, 3, 4, 5, 6, 7, 8, 9

(b) What wheel size gives you the best price?
(c) Suppose TCM is having a sale and is now charging $√

n per wheel with n digits. Now, what wheel
size gives you the best price out of the options? (again, assume that you want the capacity to be
at least 6000.)

Do your answers to parts (b) and (c) depend on the minimum capacity being 6000? In other words, would a different option be cheaper if you changed the capacity to something different than 6000? (Explain your answer in terms of $n per n-digit wheel and in terms of $√ n per n-digit wheel.