Cranes and Turtles Calculator
Solve the classic cranes-and-turtles word problem: find how many of each from the total heads and total legs, with a step-by-step solution and a check.
Input
Enter the total number of heads and legs to find how many cranes and turtles there are.
Leg counts default to 2 for cranes and 4 for turtles. Change them freely to count any two kinds of things.
Result
Answer
Cranes 3animals
Turtles 5animals
Head count check
3 plus 5 makes 8
Leg count check
2 times 3 plus 4 times 5 makes 26
How to solve it
If every animal were a turtle, the legs would total 4 times 8, which is 32.
The difference from the actual 26 legs is 26 minus 32, which is -6.
Swapping one turtle for one crane changes the legs by 4 minus 2, which is -2.
Dividing the difference -6 by -2 gives 3 cranes.
Subtracting 3 cranes from the 8 heads leaves 5 turtles.
How it works
- Assume every animal is a turtle (the one with more legs) and compute the total legs for that case.
- Find the difference between the assumed total and the actual number of legs.
- Divide that difference by the gap in legs (turtle legs minus crane legs) to get the number of cranes.
- Subtract the number of cranes from the total heads to get the number of turtles.
- Leg counts default to 2 for cranes and 4 for turtles, but you can change them for any two-item problem.
- If the numbers do not give a whole-number answer, the tool reports that there is no valid solution.
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Cranes and Turtles Calculator