### Family business

**PROBLEM 220** – The acorn doesn't fall far from the tree, as this month's problem by Rajwant Chehal of Tampa, Fla., demonstrates.

"Wonderful idea of mine, this company picnic," commented Horatio Puff, president of the Lee Key Hydraulic Co., as he strode along the grounds. "What a brainstorm to make it a family affair! The kids will recoup our expenses with all the pop and candy they buy!"

Meanwhile in another area of the picnic grounds, Lucius Bluff's two nephews were squabbling as usual.

"Give me 100 marbles, or I'll tell Uncle you broke his camera!" announced Farley. "It's only fair, because then I'll have the same number of marbles as you."

"You broke his camera, and if you don't give me 100 marbles I'll tell!" retorted Smedley. "Then, I'll have twice as many as you have left."

How many marbles does each boy start out with?

**Solution to last month's problem 219** - You put the pedal to the metal if you answered **16.6°**. Here's how Fopp fixed the game.

Let:*M _{r}* = Mass of first contestant, given as 67 kg.

*M*= Mass of bike, given as 10 kg.

_{b}*θ*= Maximum ramp angle.

*C*= Crank radius, given as 15 cm.

*T*= Tire radius, given as 34 cm.

*G*= Gear ratio =

_{r}To move uphill, the force at the rear wheel must be greater than the gravitational pull downhill.

There was an immediate, long station break after the first contestant rolled backward off the set into the audience. Fopp's $50,000 went for medical bills.

**CONTEST WINNER** – Congratulations to Gerd R. Alzuhn, P.E., of Milwaukee who won our August contest by having his name drawn from the 230 contestants who answered correctly out of a total of 336 entrants for that month. A Maple V Release 5 mathematics software package is in the mail to him.

Maple V Release 5 is an interactive computer algebra system that provides a mathematical environment for manipulating symbolic algebraic expressions, arbitrary-precision numerics, graphics, and programming. Its library features over 2,700 functions that are used in many scientific and engineering applications. Features include a MATLAB link, which lets users execute MATLAB commands from inside the software; a spreadsheet function in which Maple V operations can be performed; and an HTML export function to create web pages. The software is available in Windows 95, Windows NT, Windows 3.11, Macintosh, Power Macintosh, plus UNIX and Linux platforms.

This month's problem submitter receives an EL-546L Direct Algebraic Logic calculator from Sharp Electronics. The EL-546L has an extra-large, 10-digit, two-line LCD display that lets you see the full equation on one line and the answer to the equation on the other. An algebra and playback function enables you to enter an equation and substitute numeric values or correct errors. Another feature is the fullterm equation entry function, which enables the calculator to display a fraction equation exactly as it appears in a textbook. The EL-546L has dual power and can automatically switch from solar to battery power in low light.