The poet Longfellow, in his novel Kavanagh, introduced several clever mathematical problems from an ancient Sanskrit work.   I have used several of them in my Problems of the Week / Month.   Below is an excerpt in which the problems appear.

Excerpts from Kavanagh by Henry Wadsworth Longfellow : : "One-third of a collection of beautiful water- lilies is offered to Mahadev, one-fifth to Huri, one-sixth to the Sun, one-fourth to Devi, and six which remain are presented to the spiritual teach- er. Required the whole number of water-lilies." "That is very pretty,"said the wife,"and would put it into the boys' heads to bring you pond-lilies." "Here is a prettier one still. One-fifth of a hive of bees flew to the Kadamba flower; one- third flew to the Silandhara; three times the dif- ference of these two numbers flew to an arbor; and one bee continued flying about, attracted on each side by the fragrant Ketaki and the Malati. What was the number of the bees?" "I am sure I should never be able to tell." "Ten times the square root of a flock of geese" Here Mrs. Churchill laughed aloud; but he continued very gravely, Ten times the square root of a flock of geese, seeing the clouds collect, flew to the Manus lake; one-eighth of the whole flew from the edge of the water amongst a multitude of water-lilies; and three couple were observed playing in the water. Tell me, my young girl with beautiful locks, what was the whole number of geese?" "Well, what was it?" "What should you think?" "About twenty." "No, one hundred and forty-four. Now try another. The square root of half a number of bees, and also eight-ninths of the whole, alighted on the jasmines, and a female bee buzzed respon- sive to the hum of the male inclosed at night in a water-lily. O, beautiful damsel, tell me the num- ber of bees." "That is not there. You made it." "No, indeed I did not. I wish I had made it. Look and see." He showed her the book, and she read it her- self. He then proposed some of the geometrical questions. "In a lake the bud of a water-lily was ob- served, one span above the water, and when moved by the gentle breeze, it sunk in the water at two cubits' distance. Required the depth of the water." "That is charming, but must be very difficult. I could not answer it." "A tree one hundred cubits high is distant from a well two hundred cubits; from this tree one monkey descends and goes to the well; an- other monkey takes a leap upwards, and then de- scends by the hypotenuse; and both pass over an equal space. Required the height of the leap." "I do not believe you can answer that ques- tion yourself, without looking into the book,"said the laughing wife, laying her hand over the solu- tion."Try it." "With great pleasure, my dear child,"cried the confident school-master, taking a pencil and paper. After making a few figures and calcula- tions, he answered, "There, my young girl with beautiful locks, there is the answer, forty cubits." His wife removed her hand from the book, and then, clapping both in triumph, she exclaimed, "No, you are wrong, you are wrong, my beautiful youth with a bee in your bonnet. It is fifty cubits!" "Then I must have made some mistake." "Of course you did. Your monkey did not jump high enough." She signalized his mortifying defeat as if it had been a victory, by showering kisses, like roses, upon his forehead and cheeks, as he passed be- neath the triumphal arch- way of her arms, trying in vain to articulate, "My dearest Lilawati, what is the whole number of the geese?"

Restated, here are five of Longfellow's math problems:

1. "In a lake the bud of a water-lily was observed, one span above the water, and when moved by the gentle breeze, it sunk in the water at two cubits' distance."
Find the depth of the water.



2. "One-third of a collection of beautiful waterlilies is offered to Mahadev, one-fifth to Huri, one-sixth to the Sun, one-fourth to Devi, and six which remain are presented to the spiritual teacher."
Find the total number of lilies.



3. "One-fifth of a hive of bees flew to the Kadamba flower; one-third flew to the Silandhara; three times the difference of these two numbers flew to an arbor; and one bee continued flying about, attracted on each side by the fragrant Ketaki and the Malati.
What was the number of the bees?"



4. "A tree one hundred cubits high is distant from a well two hundred cubits; from this tree one monkey descends and goes to the well; another monkey takes a leap upwards, and then descends by the hypotenuse; and both pass over an equal space."
Find the height of the leap.



5. "Ten times the square root of a flock of geese, seeing the clouds collect, flew to the Manus lake; one-eighth of the whole flew from the edge of the water amongst a multitude of water-lilies; and three couple were observed playing in the water.
What was the whole number of geese?"


Here are the answers to those five math problems:

(1) 1.5 cubits

(2) 120 lilies

(3) 15 bees

(4) 50 cubits (assume both monkeys are at the top of the tree)

(5) 144 geese