Splitting the Herd

Winter had been unkind to Location 3. A pack of wild velociraptors — unaffiliated with Glagalbagal's operation, to be clear — had raided the hill outpost repeatedly, and Qveshna's herd had been decimated. Location 1 had fared much better, having been protected by a natural rock formation. Glagalbagal decided to redistribute the remaining animals equally across all three locations for a fresh start.

The Redistribution Problem

After accounting for winter losses, Glagalbagal's total herd stood at about a hundred and seventy animals. He needed to split this into three equal groups — one for each location.

His first instinct was to deal animals out one at a time, the way children divide sweets: one for you, one for you, one for you, repeat. But with a hundred and seventy animals and three locations, this would take nearly sixty rounds of dealing. Given Dryzk's performance with repetitive tasks (Part 8), Glagalbagal was not keen on this approach.

The Reverse

Blortz suggested thinking about it differently.

Blortz: You just learned to compute three groups of sixty. That gives you a hundred and eighty. What about three groups of fifty? A hundred and fifty. Three groups of fifty-six?

Glagalbagal: I would need to add fifty-six to itself three times. That gives... a hundred and sixty-eight.

Blortz: Close to a hundred and seventy. Try fifty-seven.

Three groups of fifty-seven: a hundred and seventy-one. One too many.

So the answer was somewhere between fifty-six and fifty-seven. Fifty-six animals per location would use a hundred and sixty-eight animals, leaving two unaccounted for. Fifty-seven per location would require a hundred and seventy-one, which was one more than he had.

The Remainder

Glagalbagal assigned fifty-six animals to each location. Two animals were left over. He stared at them — a sheep and an elderly cow — and realised there was no way to split two animals evenly among three locations without involving a butcher, which seemed excessive.

He gave one to Location 1 and one to Location 2. Qveshna protested the unfairness but was overruled on the grounds that Location 3's sparse hill terrain probably could not support an extra animal anyway.

The leftover quantity — the part that refused to divide evenly — was a new kind of result. The operation itself (finding how many groups of a given size fit into a total) was the reverse of multiplication, just as subtraction was the reverse of addition. But unlike subtraction, this reverse operation could leave something behind.

The Feed Duration

A second problem arose almost immediately. Glagalbagal had ordered a large stockpile of feed from Plyvek for the coming year — a reserve to avoid another winter crisis. He needed to know: how many months would the stockpile last?

He knew the stockpile size (a pebble arrangement representing total sacks). He knew the monthly consumption (computed using multiplication: number of animals times three sacks per animal). The question was: how many times does the monthly consumption fit into the total stockpile?

Blortz proposed a straightforward method: subtract one month's consumption from the stockpile. If there is feed left, subtract again. Count the subtractions. When you cannot subtract any more, the count tells you how many full months the feed will last, and whatever is left over is the partial remainder.

Glagalbagal performed the operation. The stockpile was large enough for three full subtractions, with a modest amount left over — enough to feed the herd for roughly ten days, but not a full fourth month.

The Mistake

Glagalbagal recorded the result: "feed sufficient for three months." He sent this to all three managers and moved on to other business.

This was the error. The feed lasted three full months, as calculated. But winter lasted four months, and the remainder — enough for ten days — was not zero. Glagalbagal had treated the calculation as if the answer were simply "three" when the actual answer was "three months and ten days."

When the feed ran out in the middle of the fourth month, Glagalbagal found himself, once again, buying emergency supplies from Plyvek. The stegosaurus was developing a permanent look of smug satisfaction.

Blortz pointed out the problem afterward.

Blortz: You computed the division correctly. You even noted the remainder. But then you ignored it.

Glagalbagal: The remainder was small.

Blortz: A remainder of ten days is not small when winter is four months. It is the difference between feeding your animals and not feeding them. You should have either ordered more feed from the start — enough for four full months — or rationed the existing feed to stretch across four months rather than consuming it at the full rate for three.

The lesson was not about arithmetic. The arithmetic had been correct. The lesson was about what you do with the result: a remainder of zero means the division is exact, but any other remainder requires a decision. Ignoring it is itself a decision — usually the wrong one.