Prev | Next
Problem #27 EASY

The Vanishing Dollar

Adobe Apple Paradoxes Logic

Problem Statement

Three colleagues split the cost of a group lunch. They hand over $30 total — $10 each. The cashier later realizes the meal was only $25 and asks a staff member to return the $5 change. The staff member, feeling mischievous, slips $2 into their pocket and hands the remaining $3 back — $1 to each colleague. Now each colleague paid $9 (since they got $1 back). Three times nine is $27. The staff member kept $2. That is only $29. Where did the extra dollar go?

Answer & Quick Explanation

Think you've got it? Click below to check your answer.

No dollar is missing. $27 (paid) = $25 (lunch) + $2 (pocketed). The staff member's $2 is already accounted for inside the $27. The riddle's final addition is a deliberate arithmetic trap — double-counting the $2.

Detailed Editorial Solution

Want to see the step-by-step breakdown? Click below to reveal the editorial.

The trick is in the final sentence of the riddle. It adds $27 (total paid by colleagues) and $2 (pocketed by staff) as though they should sum to $30. They should not — the $2 is already part of the $27. Step 1: Start: colleagues hand over $30. Cashier receives $30. Step 2: Cashier realizes overcharge: meal costs $25. Returns $5 to the staff member to give back. Step 3: Staff member pockets $2 and returns $3 — one dollar per colleague. Step 4: Each colleague effectively paid: $10 − $1 = $9. Total actually paid: $9 × 3 = $27. Step 5: Where did the $27 go? $25 went to the restaurant. $2 went to the dishonest staff member. $25 + $2 = $27. Perfect — nothing is missing. Step 6: The riddle then adds: '$27 + $2 = $29, not $30!' But the $2 is already inside the $27 — adding it again is double-counting. The correct equation is $25 + $2 + $3 = $30. Key Insight: The sleight of hand: the riddle mixes two different reference frames. '$27 paid' is the colleagues' perspective (money leaving their hands). '$2 pocketed' is already embedded within that $27. The riddle asks you to add a part to the whole that already contains it.