Logic Puzzles: Bridge Crossings, Water Jugs, Ball Weighings and Races
These puzzles train you to organize a sequence of actions under constraints, to cross a bridge, measure a volume, weigh balls or rank horses. Here are 4 riddles, each with a detailed solution.
Bridge and Torch Riddle: The Minimum Crossing Time
Classic consulting and tech interview puzzle
Four people must cross a bridge at night with only one torch. The bridge holds at most two people at a time, and the torch must accompany every crossing, so it has to be carried back when needed. They take 1, 2, 5 and 10 minutes to cross alone respectively, and a pair moves at the speed of the slower person. What is the minimum time for all four to reach the other side?
Need a hint?
Think about who should cross together with the slowest person, and who can bring the torch back without costing the slow ones extra time.
Show the answer and the solution
Answer: 17 minutes: the 1-minute and 2-minute people cross, the 1-minute person comes back, the 5-minute and 10-minute people cross, the 2-minute person comes back, then the 1-minute and 2-minute people cross again.
The reasoning
The trap is to have each slow person escorted back by the fastest one, which costs 19 minutes. The best strategy makes the two slowest people cross together, so that they do not have to come back. First, the 1-minute and 2-minute people cross together, taking 2 minutes. Then the 1-minute person brings the torch back, taking 1 minute. Next, the 5-minute and 10-minute people cross together, taking 10 minutes. The 2-minute person returns, taking 2 minutes. Finally, the 1-minute and 2-minute people cross together again, taking 2 minutes. The total is 2 + 1 + 10 + 2 + 2 = 17 minutes.
Two Jugs Riddle: Measuring 4 Liters with 3 and 5 Liter Jugs
Classic puzzle made famous by a film
You have a 5-liter jug and a 3-liter jug, both without markings, along with an unlimited water supply from a fountain. You may fill a jug, empty it, or pour the contents of one into the other until the second is full or the first is empty. How can you obtain exactly 4 liters of water?
Need a hint?
Try to get 2 liters into the large jug: that amount can then be transferred into the small one.
Show the answer and the solution
Answer: Fill the 5-liter jug and pour it into the 3-liter jug, empty the small jug, pour in the remaining 2 liters, refill the 5-liter jug and top up the small jug: 4 liters remain in the large jug.
The reasoning
Fill the 5-liter jug, then pour its contents into the 3-liter jug until that one is full. 2 liters remain in the 5-liter jug. Empty the 3-liter jug, then pour those 2 liters into it. Fill the 5-liter jug again, then pour water into the 3-liter jug, which already holds 2 liters: it accepts only 1 more liter. So 4 liters remain in the 5-liter jug.
Eight Balls and a Balance Scale: How Many Weighings?
Classic job interview question
You have eight balls that look identical, but one of them is slightly heavier than the others. You have a two-pan balance scale with no weights, which shows which pan is heavier or whether both are equal. What is the minimum number of weighings needed, in the worst case, to find the heaviest ball?
Need a hint?
Split the balls into equal groups and compare two groups: a single weighing can eliminate many of the balls.
Show the answer and the solution
Answer: At least 2 weighings: first 3 balls against 3, then either one ball against another from the group kept, or the two remaining balls against each other.
The reasoning
One weighing cannot be enough, since it has only three possible outcomes (left pan heavier, right pan heavier, or balance) while there are eight balls. So place three balls on each pan. If one pan is heavier, the heaviest ball is among the three balls on that pan: weigh two of them against each other; if they balance, it is the third one, otherwise it is the heavier of the two. If the pans balance, the heaviest ball is one of the two left aside: a last weighing compares them, and the heavier one makes its pan go down. So two weighings always suffice.
25 Horses Riddle: Finding the Fastest Three in Minimum Races
Algorithm interview puzzle: finding the best elements through successive comparisons
You have 25 horses and a track that holds 5 horses at a time. You have no stopwatch: you only know the finishing order of each race. What is the minimum number of races needed to determine the 3 fastest horses?
Need a hint?
Start by organizing the horses into groups, then ask which ones can still finish in the top three once those races are done.
Show the answer and the solution
Answer: 7 races: 5 heat races, one race between the 5 heat winners, then one race between the 5 remaining candidates.
The reasoning
The first 5 races divide the 25 horses into 5 heats of 5, whose finishing order we know. The 6th race pits the 5 heat winners against each other, and we rank them A1 > B1 > C1 > D1 > E1, each letter designating the heat of origin. A1 is the fastest horse of all, since it is the best of its heat and beats the other heat winners. For places 2 and 3, the only possible candidates are A2 and A3, the next two horses from A1's heat; B1 and B2, the winner of heat B and its runner-up; and C1. Any other horse is beaten by at least three horses and is eliminated. The 7th race, with these 5 candidates, gives the 2nd and 3rd places in the overall ranking.
Frequently asked questions
Which crossing and weighing riddles are on this page?
The page offers four puzzles: crossing a bridge with a single torch, measuring 4 litres with 3 and 5 litre jugs, weighing eight balls, and picking the three fastest horses among 25 using races of five horses each.
Do you need to be quick at arithmetic for these puzzles?
No: they mainly require organizing the steps, with simple additions and subtractions of durations or volumes. The challenge lies in the order of the actions, not in the arithmetic.
How can you get better at these logic puzzles?
Draw the starting state, list the possible actions and track the state after each step to spot dead ends quickly. Then solve the puzzle again without looking at the answer to check that the method is really learned.
What next?
Reasoning improves like memory: by practising often. Next, test yourself on our general knowledge quizzes.