Ken's blog

The host of the show, Barnstorm McDoodle, stood on an elevated podium studded with multi-colored lights. Barnstorm was wearing a jacket splattered with bright small reflectors, flashing a wide Hollywood smile under a pencil thin moustache – his thick, abundant black hair extending backwards like freshly plowed furrows in a field.

A large, transparent plastic globe full of thousands of small colored plastic balls stood in the middle of the floor between Barnstorm McDoodle and the opposing consoles of team A and B. From the globe a tube led into a small tray.

“Tonight, the contestants – Jack and Jill on my left, Mabel and Seymour on my right – can win a lot of money by guessing how many balls there are in this large globe,” announced an animated Barnstorm McDoodle, waving his arms regally to contestants and audience.

“But…if they fail…they win nothing, and the pot will be doubled for next week’s contestants,” added Barnstorm McDoodle.

“To investigate the contents of the globe, the contestants will enter numbers at their panel, to be repeated on this large screen. The number will divide all the balls in the globe into equal groups, ungrouped balls rolling out from the globe through this tube into the tray – which balls my lovely assistant Jane will fetch and replace in the globe.”

“The first team to correctly state how many balls the globe contains will win an amount in dollars equal to the number of balls,” proclaimed Barnstorm McDoodle.

“Any team can request a five minute break to work out a guess, but if it’s wrong they’ll be disqualified, so let’s get on with the show,” shouted Barnstorm McDoodle.

“But first a word from our sponsor, Ace Dogfoods.”

After Ace Dogfoods’ prolonged message, Jack and Jill entered “2” at their panel, which then appeared on the large screen. One ball rolled out into the tray and Jane stepped forth briskly on long legs to put the ball back into the globe.

“Write it all down, Jill,” said Jack.

Mabel and Seymour entered “5” and four balls rolled out into the tray, rapidly picked up and replaced by a smiling Jane.

Jack and Jill entered “6” and five balls rolled  out into the tray, Jane wiggling into action again.

“I see where this is going,” said Jack. “Let’s find a zero.”

Then, Mabel and Seymour entered an “8,” which resulted in seven balls in the tray, recovered in lithe strides by Jane.

Jack and Jill decided to take a chance and entered “11” at the panel. This time no balls came out of the globe.

“Yes!!! We request a break,” said Jack quickly, pulled out his calculator, a pen and notepad.

“Ok, folks, let’s see if Jack and Jill can guess the right number while we hear a word from our sponsor, Ace Dogfoods,” said Barnstorm McDoodle cheerfully.

“Come on Jill, use what you learned in the number theory course to figure this out rapidly before Mabel and Seymour do,” said Jack urgently. “I want to buy that motorcycle.”

“Ok, Jack, I think I see the pattern,” said Jill with a dimpled smile. “Write down what I say and get your calculator ready to win the Caribbean cruise I want.”

At the end of the five-minute word from Ace Dogfoods, Jack announced the result Jill had worked out – which, happily, turned out to be the correct number of balls in the globe.

“People, we have a winner for xxxxx dollars,” shouted Barnstorm McDoodle jubilantly, giving Jane a big hug.

What would you say was the least possible number of balls in the large globe?