Problems from Another Time - Subject Index

In addition to the subject index below, two other indices of the Problems from Another Time are available for your convenience:

Chronological Index                                      Geographical Index
 

Arithmetic

• Animal Customs (c. 180 BCE)
• Buying Wood (c. 180 BCE)
• Making Arrows (c. 180 BCE)
• Another Numbers Game (c. 400)
• Family Travels (c. 400)
• Washing the Dishes (c. 400)
• Indian Numbers Game (628)
• Be Careful Where You Step! (c. 800)
• But What's in the Flasks? (c. 800)
• Feeling Sluggish (c. 800)
• Grain and Camels (c. 800)
• Pigs in a Blanket? (c. 800)
• A Wealth of Plantains (850)
• A Tree with Branches, Nests, Eggs and Birds (1202)
• The Ant Race (1202)
• Lucky Seven (1202)
• Under Siege (1526)
• A Clothes Call (1556)
• To Each His Due (1556)
• Pepper Importation (1583)
• Long Time to Fill the Tub (1788)
• Horses and Stalls (1804)
• Nuts Over Counting (1817)
• Bargain Houses (1848)
• Harvest Time (1848)
• Hogsheads of Rum (1848)
• The Cost of War (1885)
• Traveling on a Train (1885)
• Sick Leave (1892)
• The Speculator's Buy (1892)
• A Family Problem (1905)

Algebra

Proofs

• Chuquet's Rule of Average Numbers (1484)

Pythagorean Theorem

• Circle With a Chord (c. 2000 BCE)
• Wooden Beam Against the Wall (c. 1800 BCE)
• Height and Distance (c. 250 BCE)
• Pyramid Calculation (c. 250 BCE)
• Log Stuck in a Wall (c. 100 BCE)
• The Door is Ajar (c. 100 BCE)
• Traveling Men (c. 100 BCE)
• Tree and Vine (c. 100 BCE)
• Wooden Be Board (c. 100 BCE)
• Lunchtime at the Fish Pond (629)
• Lotus in the Lake (1150)
• Monkeys in a Tree (1150)
• Poles (1202)
• Viete: Triangle (1591)
• Viete: Triangle II (1591)
• A Horse in London (1712)
• Round Pond in Rectangular Garden (1754)
• The Ruins of Persepolis (1843)
• Height of the Lighthouse (1846)
• Look Out Below! (1846)
• An Acute Problem (1869)
• Ladder Problem (1892)

Solving Cubic or higher degree Equations

• Oracle for Rent (1545)
• Square (1591)
• The Square and the Cube (1792)

Solving Equations using Proportions

• Beyond the Call of Duty (c. 100 BCE)
• Horses to Qi (c. 100 BCE)
• Silver and Gold (c. 100 BCE)
• The Rat Race (c. 100 BCE)
• Two Men Meet (c. 100 BCE)
• Water Reeds (c. 100 BCE)
• Horse of Course (c. 300)
• The Sum of Its Parts (c. 900)
• A Lion in a Well (1202)
• Loafing About (1202)
• Stinkin' Pile of Money (1225)
• A Hole in One? (1321)
• The Time It Takes To Eat a Goat (c. 1475)
• Contractors (1478)
• Out to Pasture (1571)
• Drinking Wine by the Barrel (1703)
• Free Fertilizer (1707)
• Neither Rain nor Sleet nor Snow (1728)
• A Room with a View (1790)
• A General Question (18th century)
• Age (1804)
• Bridge Over Troubled Waters (1812)
• Inheritance of Three Sons (1812)
• Provisions (1812)
• Sugar per Pound (1848)
• IOU (1856)
• Cow Dilemma (1873)
• Apples and Oranges and Peaches (1905)
• Estate Will (1905)
• Farmer's Best Deal (1905)
• Out to Pasture 2 (1905)
• Travelling Steamers (1905)
• Gun Metal (1909)

Solving Exponential Equations

• Multiplying Like Rabbits (1748)

Solving Linear Equations

• Stone Weight (c. 1800 BCE)
• Breaking Bread (c. 1650 BCE)
• Four Integers (c. 250)
• Deer in the City (c. 400)
• Faster Than a Speeding Horse (c. 470)
• Brazen Lion (c. 500)
• A Snake in the Hole (850)
• Distribution of the Mangoes (850)
• Pearls of Wisdom (c. 900)
• Elephant Hunt (1150)
• An Apple a Day (1202)
• Investing in Apples and Pears (1202)
• Small Fish (c. 1335)
• Defeated in Battle (c. 1485)
• A Game of Cat and Mouse (1494)
• On the Run (1539)
• Why It Pays to Learn Math (1608)
• A Successful Businessman (1728)
• Mystery Number (1816)
• The Cog-Wheel Revolution (1892)
• Base 7 (1902)

Solving Quadratic Equations

• The Door and the Rod (c. 100 BCE)
• The Size of a City (c. 100 BCE)
• Two Numbers (c. 250)
• Looking for Bargains (c. 900)
• Numbers Game #2 (c. 900)
• Apes in a Forest (1150)
• A Swarm of Bees (1150)
• Still More Numbers (1463)
• Numbers Game #1 (1545)
• The Recruiting Officers (1742)
• Sum of Squares (1780)
• Dimensions of a Triangle (1869)
• Sides of a Rectangle 2 (1869)
• Gardening (1885)
• Ages of Father and Son (1900)

Solving Systems of Equations

• Fields of Grain (c. 1800 BCE)
• Horsing Around (c. 100 BCE)
• Four Numbers (c. 150)
• A Basket Case (c. 400)
• Creatures with Four or Six Heads (c. 400)
• Crown of Metal (c. 500)
• Loaves and Bishops (c. 800)
• Money Makes the World Go Around (c. 820)
• Division Problem (c. 900)
• How Much to Buy a Horse? (1202)
• Purse of Denari (1202)
• Something Fishy at Customs (1202)
• Weights and Measures (1202)
• Mystery Numbers (c. 1350)
• Fine Parisian Wine (1484)
• Three Numbers in France (1484)
• Money Changers (c. 1495)
• 10 Into 3 Parts (c. 1500)
• Coins (Edo Period, 1603-1867)
• Pennies for the Poor (1608)
• Square in the Circle (1666)
• A Triangular Problem (1728)
• Difference of Squares (1728)
• To Know a Little (1728)
• Pair of Numbers (1776)
• Dealing in Sheep (1892)
• Silver Cups (1892)
• Asking a Woman Her Age (1905)
• Bicyclists on a Track (1909)
• Reverse the Digits (1909)

Calculus

Distance, Velocity and Acceleration

• Snowdrift on the Tracks (1895)

Integration

• Rifle Ball Through a Three-Inch Plank (1895)
• Woodcutter (1895)

Proofs

• Perpendicular Curves (1895)
• Series of Circles (1895)

Optimization

• Circumscribed Circle #2 (1737)
• Sides of a Rectangle (1748)
• A Circular Problem (1750)
• Conic Contents (1750)
• Maxes and Mins (1750)
• Maximization (1750)
• Steamboat (1895)
• Tomato Can (1895)
• Water Tank Minimization (1895)

Related Rates

• Man Crossing a Bridge (1895)
• What is a Bowsprit? (1895)

Series

• Triangular Numbers (1672)
• A Serious Series (1750)
• Sum of a Series (1843)

Combinatorics

• Tarrying at an Inn (1797)
• Four Companies (1829)
• Alphabet Challenge (1905)

Geometry

Area

• Inscribed Circle (c. 250 BCE)
• Square and Round Land (c. 250 BCE)
• If You Build It... (c. 820)
• Area Approximation (1220)
• In the Gentleman's Garden (1705)
• Doing Some Gardening (1738)
• Area of Elliptical Segment (1816)
• Walk Around the Triangle (1869)
• Circle, Square and Triangle (1881)
• Circumscribed Circle (1881)
• Ratio of Areas of Two Circles (1881)
• Area Problem (1899)
• Square Battalions (1905)

Circles

• Cat on a Hot Tin Wall (628)
• A Circular Problem (c. 1458)
• The Incircle of a Triangle (Edo Period, 1603-1867)
• A Grinding Stone (1709)
• Walk Around the World (1715)
• Flying High (1816)
• Landscaping (1817)
• Diameter of the Earth (1846)
• Radii of Three Circles (1869)
• Mutually Tangent Circles (1881)

Conic Sections

• Ladder Day Question (1804)

Length

• Isosceles Trapezoid (c. 2300 BCE)
• Circular Cone (1220)
• Area of an Equilateral Triangle (1730)
• Parallelepiped Chimney (1804)
• Right Triangle (1865)
• Inscribed Square (1869)

Proofs

• Heron's Formula (c. 60)
• Inscribed Circle and Trapezoid (Edo Period, 1603-1867)
• Squared Proof (1757)
• Prove the Straight Lines (1802)
• Circle and Equilateral Triangle (1804)
• Points in a Semicircle (1806)
• Area of a Polygon (1869)
• Circle and Square (1869)
• Four Circles in a Square (1881)
• Japanese Temple Problem (1892)
• A Linear Hypocycloid (1895)

Similar Triangles

• The Chinese General and the River (1247)
• Two Equal Parts of a Triangle (1817)
• Perimeters of Similar Triangles (1909)

Surface Area

• Equal Surface and Volume (1869)
• Dimensions of a Box (1909)

Volume

• Water in a Fish Pond (c. 1485)
• Three Piles of Rice (1592)
• Frustum-Shaped Mound (1627)
• Trisecting a Log (1627)
• How Much Hay? (1797)
• Loaf of Bread (1804)
• Losing My Marbles? (1846)
• Weight of a Ball (1848)
• Golden Spheres (1905)
• A Perfect Cone Sugarloaf (1905)

Interest Problems

• University Payment Plan (1556)
• Compound Interest (1848)
• Inheritance Problem (1856)

Probability

• Divide the Stakes (1654)
• What Are the Odds? (1718)
• Two Balls, No Strikes! (1814)

Trigonometry

• Height of the Clouds (1721)
• Two Circles (1755)
• Surveying a Field (1797)
• Where Cosine Meets Tangent (1804)
• A River Runs Through It (1816)
• Storm's a' Brewin' (1831)
• A Tower on a Cliff (1891)
• The Length of a String (1891)
• Three Vertical Posts (1891)