# A Tangled Tale

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Try your hand at untangling Lewis Carroll's tangled tale - one knot at a time. Each story (or knot), while amusing in its own right, contained one or more math problems for the readers to solve. You may read the separate knots, or jump straight to the questions. Attempt them at your own risk. Lewis Carroll’s replies to the original correspondents are also preserved for those who wish to compare their performance.

To My Pupil

Beloved Pupil! Tamed by thee,
Division, Fractions, Rule of Three,
Attest thy deft manipulation
Then onward! Let the voice of Fame
From Age to Age repeat thy story,
Till thou hast won thyself a name
Exceeding even Euclid’s glory.

## Knot I – Excelsior

Goblin, lead them up and down

The ruddy glow of sunset was already fading into the sombre shadows of night, when two travelers might have been observed swiftly — at a pace of six miles in the hour descending the rugged side of a mountain; the younger bounding from crag to crag with the agility of a fawn, while his companion, whose aged limbs seemed ill at ease in the heavy chain armour habitually worn by tourists in that district, toiled on painfully at his side.

As is always the case under such circumstances, the younger knight was the first to break the silence. “A goodly pace, I trow!” he exclaimed. “We sped not thus in the ascent !”

“Goodly, indeed!” the other echoed with a groan. “We clomb it but at three miles in the hour.”

“And on the dead level our pace is — ?” the younger suggested; for he was weak in statistics, and left all such details to his aged companion.

“Four miles in the hour,” the other wearily reeled. “Not an ounce more,” he added, with that love of metaphor so common in old age, “and not a farthing less!”

“’Twas three hours past high noon when we left our hostelry,” the young man said, musingly. “We shall scarce be back by supper-time. Perchance mine host will roundly deny us all food!”

“He will chide our tardy return,” was the grave reply, “and such a rebuke will be meet.”

“A brave conceit!” cried the other, with a merry laugh. “And should we bid him bring us yet another course, I trow his answer will be tart!”

“We shall but get our deserts,” sighed the elder knight, who had never seen a joke in his life, and was somewhat displeased at his companion’s untimely levity. “’Twill be nine of the clock”, he added in an undertone, “by the time we regain our hostelry. Full many a mile shall we have plodded this day!”

“How many? How many?” cried the eager youth, ever athirst for knowledge.

The old man was silent.

“Tell me," he answered, after a moment’s thought, “what time it was when we stood together on yonder peak. Not exact to the minute!” he added hastily, reading a protest in the young man’s face. “An thy guess be within one poor half-hour of the mark, ’tis all I ask of thy mother’s son! Then will I tell thee, true to the last inch, how far we shall have trudged betwixt three and nine of the clock.”

A groan was the young man’s only reply; while his convulsed features and the deep wrinkles that chased each other across his manly brow, revealed the abyss of arithmetical agony into which one chance question had plunged him.

Question: Two travelers spend from 3 o’clock till 9 in walking along a level road, up a hill, and home again: their pace on the level being 4 miles an hour, up hill 3, and down hill 6. Find the distance walked: also (within half an hour) time of reaching top of hill.

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