How to Solve Distribution Puzzles
Solve distribution aptitude puzzles by converting relative-share clues into one base-variable equation, with a worked example and practice questions.
Expected Interview Answer
Distribution puzzles ask how a fixed total of items is divided among entities under stated constraints, and the fastest reliable path is to convert every “more than / less than / twice as many” clue into a single algebraic equation in terms of one base variable, then solve the system.
Start by assigning a variable to the entity with the fewest direct constraints — often the smallest or “base” share — and express every other share relative to it. Sequential constraints ("A has 5 more than B, B has twice C") chain naturally into one variable once you substitute step by step. Always cross-check the sum of all shares against the given total, since this is the most common place an error surfaces. When the puzzle allows multiple valid distributions (open-ended, non-unique), explicitly enumerate the constraint space rather than assuming a single algebraic solution exists.
- Expressing every share relative to one base variable turns prose into a solvable equation
- Chaining substitutions handles multi-step “more/less than” clues systematically
- Cross-checking the total catches arithmetic slips before they compound
AI Mentor Explanation
A puzzle where 45 sponsorship jerseys are split among three teams — Team A has twice as many as Team B, and Team C has 5 more than Team B — is solved by setting Team B as the base variable x, so Team A = 2x and Team C = x+5. Summing x + 2x + (x+5) = 45 gives 4x = 40, x = 10, so B=10, A=20, C=15 — the exact algebraic-substitution approach that resolves every distribution puzzle regardless of the specific items being shared.
Worked example
Set base variable
- B = x
- A = 2x
- C = x + 10
Sum equation
- x + 2x + (x+10) = 90
- 4x = 80 → x = 20
Final shares
- B=20, A=40, C=30
Step-by-Step Explanation
Step 1
Choose a base variable
Assign x to the entity with the fewest direct constraints, usually the smallest share.
Step 2
Express every other share relative to x
Translate “twice as many,” "5 more," etc. into algebraic terms of x.
Step 3
Sum and equate to the total
Add all expressions and set equal to the given total to solve for x.
Step 4
Cross-check every share
Substitute x back and verify the shares sum exactly to the stated total.
What Interviewer Expects
- Correct choice of a single base variable to express all shares
- Accurate algebraic translation of “more/less/twice as many” language
- Proper chaining when constraints reference each other sequentially
- A final cross-check of all shares against the given total
Common Mistakes
- Assigning separate unrelated variables to each entity instead of one base variable
- Misreading "5 more than" as "5 times" or vice versa
- Forgetting to substitute chained relationships correctly (A relative to B, B relative to C)
- Skipping the final sum cross-check, missing a setup or arithmetic error
Best Answer (HR Friendly)
“I pick one entity as the base variable — usually whichever has the fewest constraints — and translate every other clue relative to it algebraically. "Twice as many," "5 more than," these all become simple expressions in that one variable. Once everything is expressed that way, I sum them, set the sum equal to the given total, and solve. The last step I never skip is substituting back in and checking the shares actually add up to the total.”
Follow-up Questions
- How would you handle a distribution puzzle with a non-integer solution — what does that signal?
- How do you approach a distribution puzzle where the total itself is unknown but a ratio is given?
- What changes if the puzzle allows multiple valid distributions instead of one unique answer?
- How would you extend this method to four or five entities instead of three?
MCQ Practice
1. 108 sweets are distributed among A, B and C. A gets twice B, and C gets 12 more than B. How many does B get?
x + 2x + (x+12) = 108 → 4x = 96 → x = 24.
2. What is the first step in solving a distribution puzzle algebraically?
Choosing one base variable and expressing all other shares relative to it converts the prose into one solvable equation.
3. If solving a distribution puzzle yields a non-integer share for a puzzle about whole items, what does that indicate?
Whole-item distributions must yield integer solutions; a fraction signals a setup or arithmetic mistake worth re-checking.
Flash Cards
Core technique for distribution puzzles? — Assign one base variable and express every other share relative to it algebraically.
What is the final verification step? — Substitute the solved variable back and confirm all shares sum to the given total.
How to handle chained clues (A relative to B, B relative to C)? — Substitute step by step through the chain into the single base variable.
What does a non-integer result usually signal? — An error in the equation setup or the given constraint values.