Sharewell’s Nectar Cups

Sharewell is the fairest bee in the Meadow Hive. When nectar comes in, she’s the one who pours it into the little cups for the nursery, and every cup ends up exactly the same height. Nobody gets more. Nobody gets less.

So when Middling showed the hive how to find the middle guess, Sharewell had her own idea.

“Why just pick the middle?” she said. “That ignores most of the guesses. Let’s use all of them. Pour them together and share them out evenly, like nectar.”

Comb tilted her head. “Show us.”

The question was how many wingbeats it took to fly to the brook. Five bees had flown it and made a guess: forty, fifty, fifty, sixty, and fifty.

Sharewell lined up five empty cups. “First, pour everything into one jug.” She added the guesses together, out loud. “Forty and fifty is ninety. Plus fifty, a hundred and forty. Plus sixty, two hundred. Plus fifty, two hundred and fifty.”

“Now share the jug out evenly into five cups.” Two hundred and fifty shared by five. “Fifty each.”

“Fifty,” said Comb. “And the middle guess?”

Middling lined them up: forty, fifty, fifty, fifty, sixty. “Also fifty.”

Sharewell beamed. Her way and Middling’s way agreed. It felt lovely, the way a fair share always did.

Then Farbuzz, who had been out all morning, zoomed in. “Did I miss a guess? Brook? FIVE HUNDRED!”

Sharewell hesitated. Then she added his guess in, because her whole idea was to use everyone.

“Two hundred and fifty plus five hundred is seven hundred and fifty,” she said. “Shared between six cups now.” Seven hundred and fifty shared by six. She worked it out on a leaf. “A hundred and twenty-five.”

She stared at the leaf. A hundred and twenty-five. Every bee who’d actually flown to the brook had said about fifty. Now her fair share said more than double that.

“It’s wrong,” she said quietly. “It’s not fair. One bee’s guess counted way more than everyone else’s.”

Middling lined the six up: forty, fifty, fifty, fifty, sixty, five hundred. “The two in the middle are both fifty. The middle guess is still fifty.”

Sharewell’s antennae drooped. She’d loved her idea so much.

Comb flew down beside her. “Your idea isn’t wrong. It’s just different. When all the guesses are close together, sharing them out evenly works beautifully. It even uses every bee’s information. But when one guess is way out on the end, it pours a huge amount into the jug, and your fair share gets dragged toward it.”

“So the average gets pulled,” said Sharewell slowly, “and the middle doesn’t.”

“Exactly.”

Sharewell thought about the nectar cups. If one bee poured in a whole lake of nectar, every cup would overflow, even though only one bee had done it.

“Then I’ll check first,” she said. “Before I share out evenly, I’ll look for any guess that’s miles from the rest.”

From then on, on guessing days, Sharewell and Middling always worked side by side. If her fair share and his middle guess came out close, the hive could trust them both. If they came out far apart, everyone knew to look for the guess that was pulling.