Reasoning Tests: Logic Riddles and Arithmetic Traps
These tests require you to frame the problem properly before computing, since the first instinct leads to a wrong answer in several of them. Here are 5 classic riddles, each with its solution explained.
Two Guards and Two Doors Riddle: The Question to Ask
Classic logic puzzle about truth and lies
Two doors lie before you: one leads to freedom, the other to a trap. Two guards stand in front of them; one always tells the truth, the other always lies, and you do not know which is which. You may ask only one question, to only one guard. What question should you ask to find the door to freedom?
Need a hint?
Think about including the other guard in your question, and about what each of them would do with the other's answer.
Show the answer and the solution
Answer: Ask one of the guards: “If I asked the other guard which door leads to freedom, what would he answer?” Then take the other door, the one not indicated.
The reasoning
The truthful guard and the liar both know which door leads to freedom. If you ask the truthful one what the liar would answer, he faithfully reports the wrong door the liar would point to. If you ask the liar what the truthful one would answer, he lies about the door the truthful one would point to, and again points to the wrong door. In both cases the answer points to the wrong door, so you simply take the other one.
Lily Pad Riddle: How Long to Cover Half the Pond?
Reasoning test on a quantity that doubles at each step
A lily pad doubles its surface area each day. It takes 48 days to completely cover a pond. After how many days does the lily pad cover half the pond?
Need a hint?
Work backward from the day the pond is fully covered, and ask what the surface was the day before.
Show the answer and the solution
Answer: 47 days: the day before the pond is fully covered, since the surface doubles each day.
The reasoning
If the surface doubles each day, the surface on day 48 is twice the surface on day 47. On day 47, the lily pad therefore covers exactly half the pond, since doubling half gives the whole. Intuition pushes toward 24 days, half of 48, but this is a mistake, because the growth is not linear. The lily pad therefore covers half the pond after 47 days, that is, the day before it fully covers the pond.
Bat and Ball Riddle: How Much Does the Ball Cost?
Cognitive reflection test on the trap of a quick intuitive answer
A bat and a ball cost €1.10 together. The bat costs €1 more than the ball. How much does the ball cost?
Need a hint?
Call x the price of the ball, express the price of the bat in terms of x, then write that the total is €1.10.
Show the answer and the solution
Answer: The ball costs 5 cents (€0.05), not 10 cents: the bat then costs €1.05.
The reasoning
If x is the price of the ball, the bat costs x + €1, and the total is written x + (x + 1) = 1.10, so 2x + 1 = 1.10. This gives 2x = 0.10, so x = €0.05. The ball costs 5 cents and the bat €1.05. Check: €0.05 + €1.05 = €1.10, and the bat indeed costs €1 more than the ball. The intuitive answer of 10 cents does not hold, since the bat would then cost €1.10 and the total would be €1.20.
Clock Hands Angle at 3:15: The Solution
Interview logic question on calculating angles with clock hands
What angle do the hands of a clock form at 3:15? The clock face has 12 hours and 360 degrees, and the minute hand indicates the minutes.
Need a hint?
Calculate where the hour hand is at exactly 3:00, then how far it has moved during the following 15 minutes.
Show the answer and the solution
Answer: 7.5 degrees: the minute hand is on the 3 (90 degrees) and the hour hand is at 97.5 degrees, a gap of 7.5 degrees.
The reasoning
At 3:15, the minute hand has moved for a quarter of an hour: it points to the 3, 90 degrees from the 12, since each minute is worth 6 degrees. The hour hand covers 360 degrees in 12 hours, that is 0.5 degrees per minute. At exactly 3:00 it was at 90 degrees, and during the following 15 minutes it moves 15 × 0.5 = 7.5 degrees, reaching 97.5 degrees. The gap between the two hands is therefore 97.5 minus 90 = 7.5 degrees.
Wolf, Goat and Cabbage Riddle: The River Crossing Solution
Classic logic puzzle on crossing order under safety constraints
A ferryman must cross a river with a wolf, a goat and a cabbage. His boat can carry only him and one passenger at a time. Left alone on one bank, the wolf would eat the goat, and the goat would eat the cabbage. What sequence of crossings lets him take everything across without loss?
Need a hint?
Notice the goat, which must never be left alone with the wolf or with the cabbage, and think about the order in which you take it across.
Show the answer and the solution
Answer: Take the goat across, return alone, take the wolf across, bring the goat back, take the cabbage across, return alone, take the goat across: 7 crossings.
The reasoning
The ferryman first takes the goat to the other bank, since the wolf and the cabbage cannot harm each other. He returns alone, then takes the wolf across, but immediately brings the goat back to the starting bank so as not to leave it with the cabbage. He then takes the cabbage to the other bank, where the wolf already is, and the wolf does not eat cabbage. He returns alone to fetch the goat, which is the only one left on the starting bank, and takes it across last. In total, he makes 7 crossings, and the goat is never left unsupervised with the wolf or the cabbage.
Frequently asked questions
What is a reasoning test?
A reasoning test is a short problem that pushes you to answer too fast: the answer that comes first is misleading. The five riddles on this page are examples, covering simple arithmetic and logic.
Do you need to be good at arithmetic to pass these reasoning tests?
No: the sums stay simple, and most of the work lies in how you frame the problem before counting. Reasoning about the situation matters more than the operation.
How can you avoid answering too quickly to these riddles?
Restate the riddle in your own words, note the data, then check the answer by putting it back into the statement. An answer that seems obvious deserves a check, especially when two numbers seem to cancel out.
What next?
Reasoning improves like memory: by practising often. Next, test yourself on our general knowledge quizzes.