How the goose and the stork solved the problem.

A flock of geese was flying, and one goose was flying toward them. It said, ‘Hello, one hundred geese!’ But the old goose at the front replied, ‘No, we are not one hundred geese! If there were as many of us again, plus half as many more, and a quarter as many more, then, my dear goose, there would be one hundred geese. Now, go ahead and calculate how many of us there are.

Solution

A solitary goose flew farther and pondered. Indeed, how many fellow geese had it encountered? It thought and thought, approaching the problem from every angle, yet it couldn’t solve it. Then it spotted a stork on the pond’s shore—a long-legged bird busy hunting for frogs. The stork, renowned among other birds as a mathematician, occasionally stood motionless on one leg for whole hours, lost in thought, presumably solving problems.

The goose was delighted and flew down to the pond, swimming toward the stork. It recounted how it had encountered a flock of companions, and the riddle posed by its goose-guide—a riddle that had stumped it completely. ‘Ah!’ coughed the stork. ‘Let’s try to solve it. Just be attentive and strive to understand! Do you hear?

“I’m listening, and I’ll do my best!”— replied to the goose.

“Well then. Remember what they told you? If we were to add as many geese toward us, plus half as many more, plus a quarter as many more, and you, dear goose, how many would there be? Like that?”

“Exactly!”—answered the goose.

“Now watch,”—said the stork. — “Here’s what I’ll draw for you in the sandy shore.” The stork bent its neck and used its beak to draw a line, then another line next to it, followed by half the length of that line, then a quarter of the line, and finally a tiny dash almost like a dot. It turned out the following:

The goose swam to the shore, waddled out onto the sand, looked at it, but did not understand anything.

The stork said, “Do you understand?” to which the goose replied, “Not yet!” in a gloomy tone. The stork continued, “Oh, come on! Look, as they told you: a flock, and another flock, plus half a flock, plus a quarter of a flock, and you, dear goose. So, I drew it all: a line, another line, half of that line, a quarter of that line, and even a tiny dash representing you. Got it?” The goose cheerfully responded, “Got it!”

The stork then posed a question: “If we add the flock you met to another flock, plus half a flock, plus a quarter of a flock, and you, the goose, how many would there be?” The goose confidently answered, “One hundred geese!” The stork followed up, “And without you, how many would there be?” The goose replied, “Ninety-nine.”

“Good!” said the stork. “Let’s erase the little dash representing you on our drawing and indicate that there are 99 geese left.” The stork pecked at the sand and sketched:

             The flock                                           the flock                     of the flock           of the flock      

                                                                            99 Geese

The stork continued, “Now think about it: a quarter of the flock, plus half the flock—how many quarters does that make?” The goose pondered, looked at the lines drawn in the sand, and replied, “The line representing half the flock is twice as long as the line representing a quarter of the flock. In other words, half contains two quarters. So, half plus a quarter of the flock is equivalent to three quarters of the flock.”

“Good job!” praised the stork. “Now, how many quarters are there in the entire flock?” The goose confidently answered, “Certainly, four!”

“Exactly! But here we have the flock, plus another flock, plus half the flock, plus a quarter of the flock, totaling 99 geese. So, if we translate everything into quarters, how many quarters in total?” The goose thought and replied, “The entire flock is equivalent to 4 quarters, plus another flock: another 4 quarters, making a total of 8 quarters; plus, half the flock: 2 more quarters, totaling 10 quarters; plus, another quarter of the flock: a grand total of 11 quarters, which corresponds to our 99 geese.

“Okay!” said the stork. “Now tell me, what did you ultimately figure out?”

“I’ve figured it out,” replied the goose. “In eleven quarters of the flock I encountered, there are 99 geese.” Ah, so how many geese are there in one quarter of the flock? The goose divided 99 by 11 and answered, “In one quarter of the flock, there are 9 geese.”

“Well then, how many geese are there in the entire flock?”

“In total, there are four quarters…” The goose exclaimed happily, “I met 36 geese!”

“Exactly!” solemnly declared the stork. “You probably couldn’t have figured it out on your own! Oh, you… goose!”