- Every cell has a digit from 0 to 9 or one of the four operation symbols +, −, ×, and /, signifying addition, subtraction, multiplication, and division respectively.
- No digit appears more than once in a row. No digit appears more than once in a column.
- Reading across each row, with adjacent digits concatenated into a multidigit number, the arithmetic expression yields 24.
- No + or 0 is superfluous to its arithmetic expression (e.g. at the beginning of a row). Similarly, no two operation symbols are next to one another in the same row.
- There are bold lines outlining some areas that we'll call cages.
- Each cage contains (possibly multiple copies of) + or ×, but does not contain both of those.
- Each cage's digits (not concatenated but taken one at a time), combined via + or × (whichever appears in it), yields 24.
- All the −, /, and 1 symbols are placed to get you started, as are two additional symbols.
The filled grid:
Now in row 5 the first multiplication leads to a negative number, to get to a positive value there needs to be a plus in this row. To compensate for the negative and get to 24 we need at least 2 digits after the plus fixing its position.
If the top right cage would contain an x multiplication of the number in it would always lead to a number higher than 24. Therefore it can only contain + and -. With the digits already placed there is only one way they can go there. Then the first digit in the 3rd row has to be either 2 or 4 (all 1s are already given, already a 3 in the row and with the numbers present a number in the 50s or higher would give a row sum that is too large). Because of this the topleft cage has to be a multiplication cage with only one place for the x.
The middle left cage only has two positions for numbers, so this one has to be a multiplication cage as well. Since 2, 3, 4 are already in the first column, some simple deductions can be made here. The same holds for the right middle cage. However here the digit in row three has to be 6 or 8 to assure division from 1.. by it gives a value in the 20s.
The digit in row 3 column 1 cannot be 3 since if it were three the completed expression for the row would either contain a double 6 or a double 8. This fixes the 3 at row 1 column 1. The sum of the digits in the middle cage cannot go over 24. Because of this the sum of the digits in the expression in row 3 has to stay low. The only way to achieve this from the remaining options here is as in the image below.