# Find the numbers

Here is a puzzle from the app Cryptocalc:

To solve this, you need to replace each symbol with a number from 0 to 9.

Multiple symbols cannot have the same number.

or in text form:

| 6 x 45 = 270
| x - -
| 2 x 27 = 54
| = = =
| 12 x 18 = 216

Explanation:

First column: the product of and ends in , but is not equal to . This only works if is 6 and is an even number, or is 5 and an odd number. The latter is impossible because that would make the second row 5 x 5? = ?? impossible; the product has to be three digits. So is 6.

Bottom row: the two digit numbers start with and their product is three digits. This only works if is a 1, 2; 3 would work but there's no multiple of 6 (30 / 36) that could be the first number in the bottom row.

The only even multiples of 6 that work as the bottom number in the first row are 12 and 24. If is a 4, the second row would become 4 x 4? which has three digits; one more than the last number in the second row. So is 2 and is 1.

The bottom row now reads 12 x 1? = 216, so is 8.

The last number on the second row is even (because the product is even) and non-zero (because the top right number doesn't end in a six). 4 is the only possibility, so the second row must be 2 x 27 = 54.

The factors on the top row are now known: 6 x 45 = 270.