A new December and a new bunch of puzzles from mscroggs.co.uk.

Let’s name these numbers:

abc
def
ghi

a * b + c = 46: 5*9+1, 9*5+1, 6*7+4, 7*6+4, 5*8+6, 8*5+6

a, b: 5, 6, 7, 8, 9

c: 1, 4, 6

b + e * h = 12: 3+9*1, 4+8*1, 5+7*1, 7+5*1, 8+4*1, 9+3*1, 1+5*2, 5+1*2, 1+2*4, 2+1*4

New b: 5, 7, 8, 9

e: 1, 3, 4, 5, 7

h: 1, 2

a / d / g = 1: 6/2/3, 6/3/2, 8/2/4, 8/4/2

New a: 6, 8

d, g: 2, 3, 4

Because new a and b: a * b + c = 46: 5*9+1, 9*5+1, 6*7+4, 7*6+4, 5*8+6, 8*5+6

New a: 6, 8

New b: 5, 7

Because new b: b + e * h = 12: 3+9*1, 4+8*1, 5+7*1, 7+5*1, 8+4*1, 9+3*1, 1+5*2, 5+1*2, 1+2*4, 2+1*4

e: 1, 5, 7

h: 1, 2

g – h / i = 1, g = 2, 3, 4, h = 1, 2: 3-1/2, 3-2/1, 4-1/3

New g: 2, 3, 4

i: 1, 2, 3

d, g, h and i can only be among 1, 2, 3, 4, therefore a, b, c, e and f can’t

c = 6

a = 8, b = 5

Because new a: a / d / g = 1: 6/2/3, 6/3/2, 8/2/4, 8/4/2

New d, g: 2, 4

e: 7

h = 1

i = 3

g = 4

d = 2

f = 9

856279413

The product of the red digits is 8*6*7 = 336.