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Logic Puzzles

3 Logic Puzzles With Fully Explained Solutions

A The Spare Square guide · Updated 2026-07-19 · 4 min read
3 Logic Puzzles With Fully Explained Solutions
Quick answerThese three logic puzzles use different deductions. For the mislabeled fruit boxes, draw from the box marked Mixed because that label must be wrong, then identify the other boxes by exclusion. For the arrival puzzle, Cora must be Wednesday, which forces Ben to Monday and Ada to Tuesday. For nine coins with exactly one heavier coin, weigh three against three, select the heavier group or unweighed group, then weigh one of its three coins against another. Every possible balance outcome identifies the heavier coin within two weighings.
Contents

How to use these puzzles

Read each problem, stop before its solution, and write your reasoning. The rules mean exactly what they say; no secret wordplay is waiting behind a curtain. Speed is irrelevant. A puzzle is entertainment, not a diagnostic test or a tiny courtroom deciding whether you are clever.

Puzzle one: the mislabeled fruit boxes

Three closed boxes contain apples, oranges, or a mixture of both. They are labeled Apples, Oranges, and Mixed, but every label is wrong. You may draw one piece of fruit from one box without looking inside. How can you label all three boxes correctly?

Solution

Draw from the box labeled Mixed. Because every label is wrong, this box cannot contain a mixture. If you draw an apple, that entire box must be apples; if you draw an orange, it must be oranges.

Suppose you drew an apple. Relabel that box Apples. The box currently labeled Oranges cannot be oranges, because its label is wrong, and it cannot be apples, because the apple box is known. Therefore it is Mixed. The remaining box, currently labeled Apples, must be Oranges.

If you draw an orange, the same reasoning swaps apple and orange. One draw works because the all-wrong rule turns the “Mixed” label into useful exclusion evidence.

Puzzle two: three arrival days

Ada, Ben, and Cora arrived on Monday, Tuesday, and Wednesday, one person per day.

Who arrived on each day?

Solution

Cora cannot be Monday because Ben must arrive before her. Cora also cannot be Tuesday by the third clue, so Cora arrived Wednesday.

Ben must be before Wednesday. If Ben were Tuesday, Ada would have to be Monday, contradicting the first clue. Therefore Ben arrived Monday and Ada arrived Tuesday.

The final order is Monday: Ben; Tuesday: Ada; Wednesday: Cora. Check every clue: Ada is not Monday, Ben is before Cora, and Cora is not Tuesday.

Find more checked problems in Logic Puzzles.

Puzzle three: one heavier coin

Nine coins look identical, but exactly one is heavier. You have a balance scale and may use it only twice. How do you guarantee finding the heavier coin?

Solution

Divide the coins into three groups of three: A, B, and C. First, weigh A against B.

You now have a suspect group of exactly three coins. For the second weighing, place one suspect coin on each side and leave the third off the scale.

This always succeeds in two weighings. The first weighing reduces nine candidates to three; the second reduces three to one. The method depends on exactly one coin being heavier and the scale comparing weight reliably. Change those rules and the solution may no longer hold.

Audit before celebrating

A complete solution should account for every possible outcome. The fruit solution handles either fruit drawn. The arrival solution checks all clues. The coin solution handles left heavy, right heavy, and balance at both stages.

Use the systematic solving guide for a reusable method. If your answer differs, compare assumptions before declaring either solver defeated. Sometimes the villain is simply a word interpreted two ways, wearing a very small cape.

FAQ

Why should I draw from the box labeled Mixed?

Because every label is wrong, the box labeled Mixed cannot actually contain mixed fruit. One draw therefore reveals its entire single-fruit contents. A draw from a box labeled Apples or Oranges could come from a mixed box and would not fully identify it. The universal all-wrong condition is what makes one sample sufficient.

Could Ben arrive Tuesday in the arrival puzzle?

No. Cora cannot be Monday because Ben must be earlier, and Cora cannot be Tuesday by the clue, so Cora is Wednesday. If Ben were Tuesday, Ada would be forced into Monday, contradicting Ada’s clue. Therefore Ben is Monday and Ada is Tuesday. The proposed order satisfies all three statements simultaneously.

Why divide nine coins into groups of three?

A balance scale has three possible outcomes: left side heavier, right side heavier, or balance. Groups of three let the first weighing map those outcomes to one of three equal candidate groups. The second weighing similarly maps three suspect coins to one answer. The guarantee relies on exactly one coin being heavier and all others having equal weight.

Do these puzzles measure intelligence?

No. Performance depends on familiarity, interpretation, attention, language, time, format, education, accessibility, and many other factors. The puzzles are entertainment and reasoning practice, not validated assessments of intelligence or cognitive health. Taking longer, using notes, requesting clearer wording, or disliking the format says nothing simple or reliable about a person’s ability or worth.