Lumen Lab / Logic puzzles with answers, explained step by step
Logic · 8 puzzles
Logic puzzles with answers, explained step by step
Eight original logic puzzles, roughly easiest to hardest. Each answer comes with the reasoning, because the method matters more than the answer. You’ll use the same method on the next puzzle.
1. Four drinks
Iris, Jon, Kemi, and Luis each ordered a different drink: tea, coffee, juice, or water. Tea and coffee are the only hot drinks, and the only ones with caffeine. Iris avoids caffeine. Jon ordered coffee. Kemi’s drink is hot. Luis didn’t order juice. Who ordered what?
Show the answer
Jon coffee, Kemi tea, Luis water, Iris juice. Kemi’s drink is hot and coffee is taken, so Kemi has tea. That leaves juice and water for Iris and Luis. Luis didn’t order juice, so he has water and Iris has juice.
2. The island speaker
On an island, every person either always tells the truth or always lies. Pell says, “At least one of Quinn and me is a liar.” What are Pell and Quinn?
Show the answer
Pell tells the truth, and Quinn lies. If Pell were a liar, his statement would be true, and a liar can’t say something true. So Pell is truthful, which means his statement holds: at least one of them is a liar, and it has to be Quinn.
3. Ages
Mara is twice as old as Theo. In 6 years, Mara will be 1.5 times Theo’s age. How old is Theo now?
Show the answer
6. Write M = 2T. In six years: 2T + 6 = 1.5(T + 6). That gives 2T + 6 = 1.5T + 9, so 0.5T = 3 and T = 6. Check: Mara is 12 now, and 18 is 1.5 × 12.
4. The bookshelf
Five books stand in a row: an atlas, a biography, a cookbook, a diary, and an encyclopedia. The atlas is at the far left. The encyclopedia is in the middle. The cookbook is directly to the right of the diary. Which book is at the far right?
Show the answer
The cookbook. Atlas is 1st and encyclopedia is 3rd. The diary-then-cookbook pair needs two neighboring open spots, and only 4th and 5th are left together. So the diary is 4th, the cookbook is 5th, and the biography is 2nd.
5. Exactly one is true
Exactly one of these three statements is true. (1) The key is in the drawer. (2) The key is not in the drawer. (3) The key is in the coat. Where is the key definitely not?
Show the answer
Not in the coat. Statements 1 and 2 contradict each other, so exactly one of them is always true. That uses up the one true statement, so statement 3 must be false.
6. Hidden number
I am a two-digit number. My digits add up to 11. Reverse my digits and the new number is 27 more than me. What am I?
Show the answer
47. Reversing a two-digit number changes it by 9 times the difference of its digits. 27 ÷ 9 = 3, so the second digit is 3 more than the first. Two digits that add to 11 and differ by 3 are 4 and 7. Check: 74 − 47 = 27.
7. Calendar
The day before yesterday was Thursday. What day will it be the day after tomorrow?
Show the answer
Monday. If the day before yesterday was Thursday, today is Saturday. Two days after Saturday is Monday.
8. Two trains
Train A leaves at 2:40 and the trip takes 1 hour 35 minutes. Train B leaves 25 minutes after Train A, on a route that is 10 minutes faster. When does Train B arrive?
Show the answer
4:30. Train B leaves at 3:05 and takes 1 hour 25 minutes, so it arrives at 4:30. Train A arrives at 4:15.
A method that works on almost any logic puzzle
- Start with the fixed facts. “Jon ordered coffee” or “the encyclopedia is in the middle” removes options right away.
- Look for pairs that must stay together. “Directly to the right of” gives you a block that only fits in a few places.
- Test the opposite. For truth-teller puzzles, assume the speaker lies and see if it breaks.
- Check your answer against every clue. It takes ten seconds and catches most mistakes.
Where these skills show up
Ordering, “must be true,” and hidden-rule puzzles make up a large share of the verbal and numerical sections of the Lumen Lab IQ Test. If you liked these, the full test has 24 more, all original.
Questions people ask
Are these puzzles from the real test?
No. They are written for this page so you can practice without spoiling the test itself.
Put the method to work
Twenty-four original puzzles in logic, number patterns, and visual reasoning. Taking the test is free, and you see your score range at the end.
Start the Lumen Lab IQ Test
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