I turn 30 years old tomorrow. 30 f’ing years old. CLING TO EVERY SECOND OF YOUR YOUTH. SQUEEZE EVERY OUNCE OF JOY OUT OF IT LIKE JUICE FROM YOUR FAVORITE FRUIT. SOMEDAY YOU WILL BE OLD LIKE ME.

The prize for the challenge: Free access to the PWN the SAT Math Guide Beta.

Week 1: Served customers numberedathroughbWeek 2: Served customers numberedcthroughdWeek 3: Served customers numberedethroughfWeek 4: Served customers numberedgthroughhWeek 5: Served customers numberedithroughjThe proprietor of a deli is trying to project how many customers he usually has on Mondays, so that he can order enough roast beef, but not order too much because nobody likes rotten roast beef. At the deli, customers take numbers before they are served, so he plans to collect data over the next 5 Mondays in the format of the list above, and is looking for an expression for average number of customers that he can plug numbers into as he collects them. What is the expression for the average number of customers (in terms of

athroughj) that are served in the deli on those 5 Mondays?

Good luck, children. I’ll post the solution Monday.

UPDATE: Congrats, Serrilius. I hope you enjoy the book.

As Collin so deftly pointed out in the comments, a little plugging in does wonders here. If, for example, the deli serves customers numbered 35 through 39, how many customers were served? 35, 36, 37, 38, 39. 39-35 = 4, but 5 customers were served. So when you want to know how many customers passed through on a day when numbers *a* through *b* were served, it’s *b* – *a* + 1.

So then, to find the average, you find the sum, and then divide by 5.

*b*–

*a*+ 1) + (

*d*–

*c*+ 1) + (

*f*–

*e*+ 1) + (

*h*–

*g*+ 1) + (

*j*–

*i*+ 1)]/5

*a*+

*b*–

*c*+

*d*–

*e*+

*f*–

*g*+

*h*–

*i*+

*j*+ 5)/5

*a*+

*b*–

*c*+

*d*–

*e*+

*f*–

*g*+

*h*–

*i*+

*j*)/5 + 1