In a small anthill in the middle of a large meadow lived a little ant named Philip. He was a cheerful and curious ant who had one peculiar hobby – he loved to count. He counted everything possible: pebbles around the anthill, dewdrops on grass blades, and even his own steps when he traveled in search of food.
One sunny morning he came to his ant mother and asked:
"Mommy, how many little sisters do I actually have?"
Mother smiled and stroked his head with her antennae.
"My dear Philip, in our anthill live hundreds, maybe even thousands of your little sisters. We are one big family!"
Philip's eyes widened. "So many? And can they all be counted?"
"That's a good question," Mother nodded. "Why don't you try? But remember, ants are restless and constantly moving. It won't be easy."
Philip pondered. How to count so many little sisters without making a mistake? Some work inside the anthill, others outside, still others constantly come and go. It was like counting drops in a stream.
"I need a plan," Philip said to himself and began thinking.
First, he decided to stand at the entrance to the anthill and count every ant sister who passed by. It worked for a while, but then the ants began walking too fast and some even used multiple entrances at once.
"One, two, three... oh, did I already count her? Five... no, four... or six?" Philip got confused and finally gave up. "This won't work!"
Just then his friend, a little ant lady named Lily, ran up to him.
"What are you doing, Philip? You look worried," she asked.
"I'm trying to count all my little sisters in the anthill, but there are too many of them and they keep moving. I don't know how to do it without making mistakes."
Lily thought for a moment and then suggested: "What if we divided them into groups?"
"What do you mean?" Philip asked curiously.
"Well, we could divide them according to what they do. Some are food gatherers, others are caring nurses, still others are guards... Then you could count each group separately and finally add all the numbers together."
Philip liked the idea, but still wasn't convinced. "But how do I ensure that I don't count any twice or forget some?"
At that moment, Wise Ant, the oldest inhabitant of the anthill, passed by them. When he heard their conversation, he stopped.
"I hear you have a challenging mathematical problem, young ant," he said, his antennae moving curiously.
Philip explained his problem to him.
Wise Ant smiled. "You know, Philip, many years ago I had the same idea. I wanted to know how many of us there are. Finally, I came up with a trick."
"What trick?" Philip asked eagerly.
"Marking," replied Wise Ant. "But not ordinary marking. Look, every ant gives off a certain scent – a pheromone. That's like our natural marker. What if you used small drops of sweet flower juice and gave each sister you count a tiny mark on her back?"
"But I would have to catch every single sister!" Philip objected.
"No, no," Wise Ant laughed. "You can prepare a special station – a place where they all must pass through. For example, during the evening return to the anthill. Each one who passes gets a mark, and you count how many marks you gave."
Philip brightened up. "That sounds like a great plan! But wait... what if some stay outside overnight or come through another entrance?"
"Good point," Wise Ant nodded. "You must use multiple stations and do it for several days. Or..." he pondered, "what about using our special assembly?"
"Assembly?" Lily asked in surprise.
"Yes, whenever the moon is full, all the workers return to the anthill for a special ceremony. That's when the queen issues new instructions and everyone is present."
Philip jumped with joy. "That's it! I'll count them during the assembly!"
And so Philip began preparing. With the help of Lily and Wise Ant, he created a small marking station near the main space of the anthill where the assembly was to take place. He prepared sweet dandelion juice mixed with a bit of powder from colorful flowers so the mark would be clearly visible.
On the day of the assembly, Philip positioned himself at his station and began his important task. Every little sister who passed got a small dot on her back and Philip made a mark in his notebook made from a leaf.
But soon he discovered that it was too much work for one ant.
"I need help!" he called out.
Lily immediately rushed over and began helping with the marking. Wise Ant devised a system for counting the marks – for every ten ants he made a line on the leaf.
The work went smoothly, but it was still difficult to keep track. At one point the sweet juice ran out and they had to quickly prepare more. Other times several sisters passed too quickly and they didn't manage to mark them.
"This is harder than I thought," Philip sighed as he tried to keep pace with the stream of ants.
"Maybe we need a better system," Lily suggested.
"What about dividing them into smaller groups?" said Wise Ant.
And so they divided the entrance to the assembly space into five smaller corridors. At each corridor stood one helper – Philip, Lily, Wise Ant, and two other friends they invited to help.
Each one marked and counted the ants passing through their corridor. They agreed on a clear signal – for every 10 ants they raised a leg, and for every 100 they waved their antennae. This way Philip had an overview of how many ants had already passed through each corridor.
When the assembly ended, everyone met to count the results.
"Exactly 127 ants passed through my corridor," Philip announced.
"I counted 98," said Lily.
"I had 145," announced Wise Ant.
The other two helpers reported 112 and 103 ants.
Philip began calculating: "So 127 plus 98 is 225, plus 145 is 370, plus 112 is 482, and plus 103 is altogether 585 ants!"
"But wait," Wise Ant pondered. "Are we sure that each sister passed only once and that we didn't forget any?"
Philip scratched behind his antennae. "That's a good question. How can we be sure?"
"I have an idea," Lily exclaimed. "What if we did it again, but this time we used a different color for the marks? We'll compare whether we get the same number."
And so the next day they prepared a new set of colors and repeated the whole process. This time they counted 579 ants.
"Almost the same number!" Philip exclaimed enthusiastically. "That means our counting is quite accurate."
"But why is there a difference of six ants?" Lily asked.
Wise Ant pondered. "Maybe some sisters were on a longer expedition and were missing yesterday, while others stayed in the anthill today to care for larvae."
Philip nodded. "That makes sense. So I have approximately 580 little sisters!"
"Exactly," Wise Ant praised him. "In mathematics we sometimes can't get a completely precise number, especially when counting something that's constantly changing. But we can get close to it using good methods and repeated measurements."
Philip was immensely proud of his success. He ran to his mother to announce the result.
"Mommy! I have approximately 580 little sisters! I counted them!"
Mother hugged him with her antennae. "That's wonderful, Philip! And how did you manage it?"
Philip enthusiastically told her about his method, about marking, about dividing corridors and repeated counting.
"You know, Mommy," he added proudly, "I learned that even when something is almost impossible to count, with a good plan and help from friends, it can be done!"
And from then on, Philip was known in the anthill not only as a curious little ant, but also as the one who managed to count his entire large family. And he discovered that the greatest joy wasn't in the exact number, but in the journey of how he arrived at it.