In the image above each symbol represents a different non-zero single-digit number . In the second and third equation for example, we have a single-digit number times a single-digit number that is equal to a two-digit number .
What is the value of ?
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In the first equation we have that ★ × ★ is equal to a single-digit number. So it can only be the numbers 1 , 2 or 3 . It can't be 1 because 1 × 1 = 1 and the star and the club suit are different digits. It can't be 2 too, because in the second equation we have a two-digit number as the result and 2 × 4 = 8 which is not possible. Hence, ★ = 3 and ♣ = 3 × 3 = 9 .
In the second equation we have ★ × ♣ = 3 × 9 = 2 7 . Hence, ⧫ = 2 and ♠ = 7 .
In the third equation we have 7 × ♡ = ♢ ⊙ . The only numbers available now that creates a two-digit number when multiplied by 7 are 4 , 5 , 6 and 8 :
7 × 4 = 2 8
7 × 5 = 3 5
7 × 6 = 4 2
7 × 8 = 5 6
The only possibility that don't repeat any number is when ♡ = 8 . Hence, ♢ = 5 and ⊙ = 6 .
The answer for this question is ♡ × ⊙ = 8 × 6 = 4 8