Apologies for the short delay in posting an answer folks – being at the other end of the country with only a phone to my name made it somewhat tricky to get the solution up! But never fear, it’s here now. If you recall, your puzzle for this week was to work out the value of the fourth column…

So, to work this one out you had to employ a little simple algebra. By turning the colours of the circles into letters, we can do this very easily:

- Black = B
- Grey = G
- White = W

We can now make equations out of the columns:

- 2G + 2W = 68
- B + 2G + W = 47
- B + G + 2W = 61
- 3B + G = ?

The next step is to work out the values of each letter. You could really do this in any order, but I’m going to work out G first, by finding W and B in terms of G.

Taking the first equation:

2G + 2W = 68

G + W = 34

W = 34 – G

Taking the third equation (arbitrarily):

B + G + 2W = 61

B = G – 7

B + G + 2(34 – G) = 61

B + G + 68 – 2G = 61

B – G = -7

Now we can take the second equation:

B + 2G + W = 47

(G – 7) + 2G + (34 – G) = 47

G – 7 + 2G + 34 – G = 47

2G + 27 = 47

2G = 20

G = 10

The equation we will eventually work out only contains B and G, so we now need to find B – however, all the equations involving B also involve W, so we actually need to calculate W first.

Taking the first equation again:

2G + 2W = 68

G + W = 34

10+ W = 34

W = 24

Now we can take either the second or the third equation, and find B. I’ll use the second:

B + 2G + W = 47

B + 20 + 24 = 47

B = 3

Now we take the fourth equation and just plug in our values!

3B + G = ?

9 + 10 = ? = 19

So how’d you do?

Vel.

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