The Collection
Every logic puzzle here is machine-checked by a solver before it is published: one provable solution, no ambiguous clues. Classic imports from the public domain are labeled until they pass review.
Showing 14 of 14 puzzles
Nicarete's Nuts
Nicarete shared out her nuts: a third to Cleis, a quarter to Sappho, a fifth to Aristodice, a twentieth and a twelfth to Theano, and a twenty-fourth to Philinnis. That left her 50 nuts. How many did she start with?
The Shared Apples
A girl shared out her apples: a fifth to Chrysis, a fourth to Hero, a nineteenth to Psamathe, a tenth to Cleopatra and a twentieth to Parthenope; twelve went to Evadne, and she kept 120 for herself. How many apples were …
The Bronze Lion
I am a bronze lion, and my spouts are my two eyes, my mouth, and the flat of my right foot. My right eye fills a jar in 48 hours, my left eye in 72 hours, and my foot in 96 hours. My mouth fills it in 6 hours. How long d…
The Rectangular Field
A rectangular field covers 864 square paces, and it is 12 paces longer than it is wide. How wide is the field?
The Door and Its Diagonal
A door is 6.8 feet taller than it is wide, and its diagonal measures 10 feet. How wide is the door?
The Remainder Problem
Find the smallest whole number that leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by 5, and a remainder of 2 when divided by 7.
The Weaving Woman
A woman weaves 5 feet of cloth on the first day, and each day after that she weaves the same amount less than the day before, until she weaves 1 foot on the thirtieth and last day. How much cloth does she weave altogethe…
The Sea Island
Two poles 30 feet high stand 1,000 paces apart, in line with an island out at sea. An observer who walks 123 paces back from the near pole sees the island's summit in line with the top of that pole. Walking 127 paces bac…
The Three Sisters
Three sisters come home every 5, 4 and 3 days. Today all three are at home together. In how many days will they next all be at home on the same day?
The Broken Bamboo
A bamboo 10 feet tall snaps part way up, and the top touches the ground 3 feet from the foot of the stem. How high above the ground is the break?
Three Classes of Corn
Three bundles of first-class corn, two of second class and one of third yield 39 measures. Two of first, three of second and one of third yield 34 measures. One of first, two of second and three of third yield 26 measure…
Buying It Together
A group of people are buying something between them. If each puts in 8 coins they have 3 coins too many; if each puts in 7 they are 4 coins short. How many people are in the group?
The Hare and the Hound
A hare is 100 paces ahead of a hound. The hound chases it for 250 paces, and by then only 30 paces separate them. How many more paces must the hound run to catch the hare?
The Good Runner and the Bad Runner
A good runner covers 100 paces in the time a bad runner covers 60. The bad runner starts 100 paces ahead. How many paces must the good runner run to draw level with him?
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