Number Chain Trivia Quiz

The following is just one way to start solving this. It is a similar situation to the horizontal equation going through (E,1) which was only missing one number. In this case, the horizontal equation is the first one on line 5 which is ? - 5 = -2. When you move the 5 to the other side of the equation, this becomes ? = -2 + 5 to which the answer is the number 3.

The vertical equation in column A is now solvable, having placed the number 3 at (A,5). The equation is 12 / by ? = 3. Rearranging the equation gives 12 / 3, the answer to which is the number 4.

Moving to the horizontal equation through (E,1), it was revealed in the introduction that the number here is 14. This now makes the vertical equation through (E,1) solvable, namely 14 - ? = -2. Swapping the unknown with the -2 gives the equation 14 - -2 = ?, which means that the number 16 is at (E,3).

Having found that the number 16 goes at (E,3), the horizontal equation going through (E,3) can be solved. The equation is ? + 16 = 29. Rearranging this gives 29 - 16 which means the number 13 goes at the location (C,3).

Having found the number 13 at (C,3), the vertical equation through (C,3) can be solved. The missing number at (C,7) is the answer to the equation 13 - 5 which is 8. This sets up the next equation, the horizontal one through (C,7).

The number at (E,7) is the next obvious one to solve. Having placed the number 8 at (C,7), the equation is 8 = ? + 9. Moving the 9 to the other side of the equation and changing its sign gives -1 as the number at (E,7).

Placing -1 at (E,7) means that the vertical equation passing through (E,9) is -2 x -1. The minus signs cancel out and so it gives the number 2 at (E,9).

The vertical equation in column G was one of the three equations that could be solved at the outset. The equation is 29 - ? = 9. Rearranging the equation gives 29 - 9 and the answer of the number 20 at (G,5).

Having worked out that the number 20 goes at (G,5), the horizontal equation through (I,5) can be solved. The equation is -2 + 20 which gives the number 18 at (I,5).

The easy equations have been solved leaving two equations both with two number missing, although only three numbers are left. As the remaining numbers are whole numbers, the vertical equation in column I must also produce a whole number answer. This means that the number 18 in (I,5) must be divided by either the -3 or the -6 as dividing 18 by 5 gives 3.6 which is not a whole number.

So that means that number 5 is not part of the vertical equation through column I and must go at (G,9) in the horizontal equation in line 9.

Having worked out that the number 5 goes at (G,9), the horizontal equation on line 9 can be solved. The equation is 2 = 5 + ? This can be rearranged to be ? = 2 - 5 which means the number -3 goes at (I,9).

Having found the numbers for (I,5) and (I,9) as 18 and -3 respectively, we can now solve the vertical equation which goes on column I. The equation is 18 / ? = -3. The equation can be rearranged to be 18 / -3 = ? The answer is the number -6 which goes at (I,7) and completes the grid.