Cryptarithmetic Questions for Infosys and eLitmus

Cryptarithmetic is a class of puzzle where each letter in an arithmetic equation stands for a unique digit, and the equation must hold when you substitute digits for letters.

Two companies in particular use this kind of puzzle in their selection process: Infosys, through the reasoning section of its aptitude test, and eLitmus, whose pH Test includes a problem-solving module with exactly this type of constraint puzzle. Knowing the mechanics before you sit either test saves the time that would otherwise go toward unstructured guessing.

What is Cryptarithmetic?

Take the equation SEND + MORE = MONEY. Every distinct letter is a distinct digit from 0 to 9. No two letters share the same digit. The leading letter of any multi-digit number cannot be zero, so S and M cannot be 0. Exactly one assignment of digits satisfies the equation.

That last point matters. A well-formed cryptarithmetic puzzle has only one valid solution. If you find two possible assignments, you missed a constraint or the puzzle is poorly written. In an exam, assume one solution exists and stop searching once you have it.

The Four Rules

Every cryptarithmetic puzzle operates under four rules. Getting one wrong leads directly to the wrong answer.

• Unique digits. Each letter represents a different digit. If P = 4, no other letter equals 4.
• No leading zeros. The leftmost letter of any number cannot equal 0. In SEND + MORE = MONEY, neither S nor M can be zero.
• One valid solution. A correctly written puzzle has exactly one answer. This is both a constraint and a shortcut: once your logic eliminates all but one assignment, you are done.
• Arithmetic holds. Once you substitute all digits, the equation must be numerically correct. Double-checking with the final numbers catches errors that crept in during analysis.

SEND + MORE = MONEY: A Worked Solution

This is the most commonly cited cryptarithmetic puzzle in placement preparation. Older articles on this topic list it without actually solving it. Here is the complete derivation using carry analysis.

The addition aligns as:

  S E N D
+ M O R E
---------
M O N E Y

• Step 1 — Determine M. SEND and MORE are both 4-digit numbers. Their sum, MONEY, is a 5-digit number. The only carry that can generate a fifth digit is 1. So M = 1.

• Step 2 — Analyse the thousands column. S + M + c3 = O + 10 times M, where c3 is the carry from the hundreds column. Substituting M = 1: S + 1 + c3 = O + 10, which means S + c3 = O + 9.

• Step 3 — Two cases for c3. If c3 = 0: S minus O = 9, giving S = 9 and O = 0 (the only single-digit pair with a difference of 9). If c3 = 1: S minus O = 8, giving either S = 9, O = 1 (conflict: M already equals 1) or S = 8, O = 0.

• Step 4 — Eliminate the c3 = 1 case. Move to the hundreds column: E + O + c2 = N + 10 times c3. With O = 0 and c3 = 1: E + c2 = N + 10. The maximum of E + c2 is 9 + 1 = 10, so N = 0. But O = 0 and N cannot also be 0. The c3 = 1 sub-case is impossible. Therefore: S = 9, O = 0, c3 = 0.

• Step 5 — Hundreds column with c3 = 0. E + 0 + c2 = N + 0, so N = E + c2. N is either equal to E (if c2 = 0) or E + 1 (if c2 = 1).

• Step 6 — Tens column. N + R + c1 = E + 10 times c2. Substituting N = E + c2 gives R + c1 = 9 times c2. If c2 = 0: R + c1 = 0, so R = 0 = O, which is a conflict. If c2 = 1: R + c1 = 9. Since S = 9, R cannot equal 9. So R = 8, c1 = 1, and N = E + 1.

• Step 7 — Units column. D + E = Y + 10 times c1 = Y + 10. So Y = D + E minus 10, confirming c1 = 1 produced a carry.

• Step 8 — Assign remaining digits. Digits used so far: M = 1, S = 9, O = 0, R = 8. Remaining pool: {2, 3, 4, 5, 6, 7} for E, N = E + 1, D, Y.

  Testing each valid (E, N) pair from consecutive values in the remaining pool:

  • E = 2, N = 3: D must satisfy D + 2 = Y + 10, so D is at least 8. Not available in pool. Ruled out.
  • E = 3, N = 4: D = 7 gives Y = 0, which equals O. Ruled out.
  • E = 4, N = 5: D = 6 gives Y = 0 = O. D = 7 gives Y = 1 = M. Both ruled out.
  • E = 5, N = 6: D = 7 gives Y = 2. Both 7 and 2 are in the remaining pool and distinct from all assigned digits. Valid.
  • E = 6, N = 7: D = 4 gives Y = 0 = O. D = 5 gives Y = 1 = M. Ruled out.

• Final assignment: M = 1, O = 0, R = 8, S = 9, E = 5, N = 6, D = 7, Y = 2.

• Verification: SEND = 9567, MORE = 1085, MONEY = 10652. Addition: 9567 + 1085 = 10652. Correct.

Where These Questions Appear in Infosys and eLitmus

Infosys screens freshers through three tracks with distinct difficulty levels.

Track	Starting CTC	Reasoning Difficulty
System Engineer (SE)	₹3.6 LPA	Standard aptitude: series, analogies, basic puzzles
Specialist Programmer (SP)	₹6.5 LPA	Stronger focus on logical deduction and data structures
Power Programmer (PP)	₹9.5 LPA	Advanced reasoning; InfyTQ and HackWithInfy performance weighted

Cryptarithmetic-style questions most often appear at the SP and PP levels, where logical deduction is evaluated more rigorously. The SE test covers standard aptitude without puzzle-heavy variants.

According to Q4 FY26 commentary by Infosys CEO Salil Parekh, Infosys offers different starting compensation for candidates with AI-attuned skills and is building a pool of forward-deployed engineers to do more AI solution work directly with clients. The harder aptitude tracks are where that pool gets identified.

On the eLitmus side, the pH Test covers three sections: Maths, Reasoning, and Verbal. Cryptarithmetic appears in Reasoning. The test is used by a range of product and mid-tier companies for off-campus hiring. See the eLitmus pH Test complete guide for the full syllabus breakdown.

Five Strategies for Solving Under Time Pressure

Apply these in sequence when a puzzle appears on-screen.

• Start with the leading digit of the longest number. If the result has one more digit than either operand, a carry generated that digit. In SEND+MORE=MONEY, this immediately gives M = 1 with no arithmetic required.
• Track carries column by column. Label each carry c1, c2, c3. Carries are binary (0 or 1). Two unknowns plus a binary carry is manageable in two cases, not hundreds.
• Look for columns with one unknown. Once enough digits are assigned, some columns have only one letter remaining. Solve those first, they feed constraints into adjacent columns.
• Eliminate early, enumerate late. The carry approach turns a nine-factorial search space into a handful of cases. Enumerate only after constraints have narrowed the field to a small set of candidates.
• Verify with the full equation. Substituting back and checking the arithmetic takes under 30 seconds. It catches transcription errors that would otherwise invalidate a correct analysis.

For more practice questions and full solutions, the Infosys placement papers collection and the Infosys interview preparation guide cover the broader aptitude and technical sections alongside cryptarithmetic.

Constraint Elimination and the AI Connection

The carry-analysis approach to SEND+MORE=MONEY, which turns a nine-factorial search into a 30-second deduction, is the same skill that shows up in AI engineering: narrowing a solution space by ruling out impossibilities before enumerating candidates. Feature selection, search algorithm design, and LLM output debugging all run on that same logic.

TinkerLLM is where students can build that intuition on real LLM problems at ₹299, starting with the same constraint-first thinking the cryptarithmetic section tests. The AI roadmap breaks down the curriculum without the enrolment commitment.