Fill The Blanks Equation Solver

A fill in the blank puzzle is a mathematical exercise similar to equations solving. It is necessary to find the missing elements (the blanks) in the proposed maths problem so that it becomes correct.

Fill in the blanks with missing digits

Example: Find the missing numbers in the addition 78? + 4? 6 + 123 =? 321 has for solution 782 + 416 + 123 = 1321

Sometimes there is more than one possible solution in operations with blanks.

Example: Find the missing numbers in the subtraction 45 - ?2 = ?3 has 5 solutions including: 45 - 12 = 33 or 45 - 32 = 13

Be sure to indicate a question mark for each digit, else see the equation solver.

Example: 12 + ? = 34 has no solution but 12 + ?? = 34 has one 12 + 22 = 34

Fill in the blanks with missing operators

The principle is the same, except that the question marks must be replaced by one of the 4 mathematical operators (+, -, *, /)

Example: 1 ? 2 ? 3 = 0 has several solutions including 1 + 2 - 3 = 0

If the order of the numbers can be changed, see the countdown numbers solver.

Manual resolution involves identifying the most likely replacement elements. A first approach is to list all the possibilities of each blank, then if the value can not be determined, make attempts until finding the answer. Here are some techniques:

Fill in the blanks with missing digits

Look at the unit numbers, how to add / subtract / multiply them and list the possibilities.

Identify remarkable values: a multiplication by 2 gives an even number, a multiplication by 5 gives a number ending by 0 or 5, and so on.

Identify impossible values: divisions by 0 or non-integers, and so on.

Fill in the blanks with missing operators

Filter operations: division is rare, multiplication introduces large numbers, etc.

Look at the numbers of the units, how to add / subtract / multiply them and list the possibilities.

dCode uses computer techniques that allow you to quickly attempt all combinations.