Medium
Logical Puzzles
Test deduction, reasoning and logical thinking skills.
Logical Puzzles Puzzles
Hard
Five students P, Q, R, S and T scored different marks. P scored more than Q but less than R. S scored less than Q. T scored more than R. Who scored the highest and who scored the lowest?
Hard
Four tasks W, X, Y and Z must be completed one at a time. W must be before X. Y must be before Z. X must be before Y. Which task must be completed third?
Expert
Seven runners finish a race. A finishes before B. B finishes before C. D finishes after C. E finishes before A. F finishes after D. G finishes before E. Who must finish before everyone else?
Medium
A library has books numbered 1 through 50. Every fifth book is placed on a special shelf. How many books are on the special shelf?
Medium
Five people A, B, C, D and E stand in a line. A is immediately before B. C is somewhere after B. D is at the extreme right. E is not next to D. Who must be at position 3?
Hard
Four people A, B, C and D must sit in four consecutive seats. A cannot sit next to B. C must sit immediately to the left of D. How many valid arrangements are possible?
Medium
A box contains red, blue and green balls. There are more red balls than blue balls and more blue balls than green balls. If there are 9 balls in total and each color has at least one ball, how many possible distributions are there?
Hard
Three friends A, B and C have different heights. A is taller than B. C is shorter than A but taller than B. Who is tallest and who is shortest?
Hard
Six books P, Q, R, S, T and U are arranged on a shelf. P is before Q. R is immediately after S. T is after Q. U is before P. Which of the following must be true?
Medium
A meeting has four speakers: A, B, C and D. A speaks before B. C speaks after B. D speaks before A. What is the only possible order?
Hard
Seven cards numbered 1 through 7 are placed face down. If card 1 is immediately before card 2 and card 3 is immediately before card 4, how many arrangements are possible?
Expert
A farmer must cross a river with a wolf, a goat and a basket of grain. The boat can carry the farmer and only one of the three at a time. The wolf cannot be left alone with the goat, and the goat cannot be left alone with the grain. How can the farmer transport all three safely?
Hard
A code consists of three different digits. The first digit is twice the second. The third digit is one more than the second. If the sum of the digits is 10, what is the code?
Medium
A sequence of lockers is numbered 1 to 30. Every third locker is painted blue, starting with locker 3. How many blue lockers are there?
Medium
Three switches are outside a closed room. Inside the room is one light bulb. Only one switch controls the bulb. You may manipulate the switches as much as you want, but you may enter the room only once. How can you identify the correct switch?
Hard
You have 12 coins. One coin is counterfeit and may be either heavier or lighter than the others. Using a balance scale, what is the minimum number of weighings needed to identify the counterfeit coin and determine whether it is heavier or lighter?
Medium
A farmer has chickens and rabbits. There are 20 heads and 56 legs in total. How many chickens and rabbits are there?
Hard
A person has exactly 7 litres of water but only a 5-litre and a 3-litre measuring jug. How can the person measure exactly 4 litres?
Medium
A, B and C are standing in a line. A is not first. B is not last. C is to the right of A. What is the only possible order?
Medium
There are five boxes in a row. The red box is immediately to the left of the blue box. The green box is somewhere to the right of the yellow box. The black box is at the left end. If the red box is in position 3, where is the blue box?
Expert
You have 100 prisoners and 100 boxes. Each box contains one prisoner number, randomly arranged. Each prisoner may open at most 50 boxes and must find their own number. They cannot communicate after the process begins. What strategy gives a substantially better chance than random independent searching?
Medium
A bus has exactly 40 passengers. At the first stop, 12 get off and 7 get on. At the second stop, 9 get off and 5 get on. How many passengers are on the bus after the second stop?
Hard
A sequence starts with 2. Each new term is obtained by multiplying the previous term by 2 and subtracting 1. What is the fifth term?
Medium
You have two ropes. Each rope takes exactly 60 minutes to burn completely, but neither rope burns at a uniform rate. How can you measure exactly 45 minutes?
Hard
You have an 8-litre jug, a 5-litre jug and a 3-litre jug. The jugs have no measurement markings. Using only these jugs, measure exactly 4 litres.
Medium
There are 100 closed lockers. On pass 1, every locker is opened. On pass 2, every second locker is changed. On pass 3, every third locker is changed, and so on until pass 100. Which lockers remain open?
Hard
A, B and C are either truth-tellers or liars. A says, "B is a liar." B says, "A and C are of the same type." C says, "B is a liar." Who is truthful?
Medium
A person has four identical-looking keys and four identical-looking locks. Each key opens exactly one lock. What is the minimum number of individual key-lock tests needed in the worst case to guarantee matching every key to its lock?
Hard
Three boxes contain coins. One box contains only gold coins, one contains only silver coins, and one contains a mixture. Every label is wrong. You may take one coin from one box. Which box should you choose?
Medium
A farmer needs to transport three identical sacks across a narrow bridge. The bridge can support the farmer and only one sack at a time. Each crossing takes 2 minutes. The farmer starts and finishes on the same side after transporting all three sacks. What is the minimum total time?
Hard
You have 9 visually identical coins and exactly one is heavier. Using a balance scale, what is the minimum number of weighings required to guarantee finding the heavier coin?
Expert
Four people need to cross a bridge at night. Their crossing times are 1, 2, 5 and 8 minutes. At most two can cross at once and they must carry one torch. What is the minimum total time?
Medium
You have three boxes. One contains only apples, one contains only oranges, and one contains both apples and oranges. All three boxes are incorrectly labeled. You may pick exactly one fruit from exactly one box without looking inside. How can you correctly label all three boxes?
Hard