Enter your five Krypto cards and the objective number below. The solver exhaustively searches every permutation, operator combination, and parenthesization to find all valid solutions — not just one. Standard deck rules are enforced by default; use the options to relax constraints for house-rule play. After solving, hover any result to reveal a step-by-step breakdown that walks through the calculation one operation at a time.
Standard rules: Use each of the 5 cards exactly once with +, −, ×, ÷ to equal the objective. Deck composition: 1–6 (×3 each), 7–10 (×4 each), 11–17 (×2 each), 18–25 (×1 each).
How to Play Krypto
Krypto is a mental arithmetic card game first published in 1963. A dealer turns up five cards and one objective card from the special 56-card deck. Each player races to find any arithmetic expression that uses all five card values exactly once — combined with addition, subtraction, multiplication, and division in any order with any parenthesization — that evaluates to the objective number.
The first player to announce a valid solution wins the hand. In standard play, all intermediate values must be positive integers, though many groups relax this for younger players or harder hands.
How to Use This Solver
- Type your five card values into the Card 1–5 fields.
- Enter the Objective number.
- Click Find Solutions (or press Enter).
- All valid expressions are displayed in a grid. Solutions are deduplicated — commutative and associative equivalents are shown only once.
- Hover (or tap) any solution to reveal the ≡ breakdown button. Click it to see the equation solved step by step.
The solver returns up to 200 distinct solutions. The N label flags solutions that use a negative intermediate value; F flags solutions that use a non-integer intermediate value. These are only shown when the corresponding option is checked.
Solver Options Explained
- Allow any number (<200): Disables the standard deck validation so you can enter any card values from 1–199. Useful for custom or extended Krypto variants.
- Allow negative intermediates: Permits steps like 3 − 7 = −4 en route to the objective, even though the final answer must still be positive. Expands the solution space significantly.
- Allow fractional intermediates: Permits non-integer intermediate results such as 7 ÷ 2 = 3.5, provided the final answer is still a whole number matching the objective.
About the Krypto Deck
The standard Krypto deck contains 56 cards distributed as follows:
- Cards 1–6: 3 copies each (18 cards)
- Cards 7–10: 4 copies each (16 cards)
- Cards 11–17: 2 copies each (14 cards)
- Cards 18–25: 1 copy each (8 cards)
The deck composition means you can hold duplicate cards in a hand, two 3s for example, as long as the total count across all six cards (the five dealt plus the objective) does not exceed the deck count for that number. The solver enforces this rule automatically when standard mode is active.
Frequently Asked Questions
What is the card game Krypto?
Krypto is an arithmetic card game published by MPH Games. Players are dealt five number cards and one objective card. The goal is to combine the five cards using addition, subtraction, multiplication, and division to arrive at the objective.
How do you solve Krypto?
Try every permutation of the five cards with every combination of the four arithmetic operators and every valid parenthesization. That's up to 5! × 4⁴ × 14 = over 300,000 possibilities per hand. This solver automates the exhaustive search and returns all valid expressions instantly.
What if there is no solution?
Most Krypto hands have at least one solution, but rare combinations are unsolvable under strict rules. This solver will report "No solutions found." Try enabling fractional or negative intermediate values to find extended solutions.
Can I use fractions or negative numbers?
Standard rules require positive whole-number intermediate results. Many groups play with house rules that allow fractions or negatives on the way to the objective. Both variants are supported via the checkboxes above the Solve button.
Is this solver free?
Yes! Completely free, no login required. It runs entirely in your browser with no data sent to any server.
What is the step-by-step breakdown?
Each solution has a hidden ≡ button that appears when you hover over it (or tap on mobile). Clicking it opens a panel showing the expression evaluated one operation at a time — innermost parentheses first — so you can follow exactly how the result is reached. The final step is highlighted in red.