Calculating Crosses Trivia Quiz

The easiest equations to start with are those where there is only one number missing from the equation. At label 1, the vertical equation (reading down) is 10 + ? = 25. The missing number of 15 can be calculated by subtracting the 10 from the 25. Others in this category are the vertical equations for labels 3 and 6.

As a result of solving labels 3 and 6, labels 4 and 7 can be solved. Having solved label 4, label 5 becomes possible. Similarly, solving label 1 allows label 2 to be solved.

Having worked out that label 1 is the number 15, this gives the equation 15 / 5 = ?. The answer is 3 so the number 3 needs to be placed against label 2. This helps us solve the numbers going at labels 8 and 9, as explained later.

The equation to find the number for label 3 is only missing one number. This means that it is simply the total of 3 + 17 which is 20. This allows us to solve label 4 next.

Solving the equation for label 3 gives us the ability to solve the equation for label 4. Label 3 is the number 20 so the equation to be solved is ? + 20 = 30 or 30 - 20 = ? The answer is 10. This in turn allows us to solve the number for label 5.

We can solve this one by solving the number going against label 3 first. This proves to be 20. This in turn allows us to solve label 4, which is the number 10. This gives the vertical equation of 46 - ? = 10 for label 5. This is solved with the number 36 at label 5.

Label 6 is part of a vertical equation just missing the one number. The equation is 30 / 30 or 30 divided by 30 which is the number 1. This allows us to solve the horizontal equation ? - 5 to get the number for label 7. It also removes the number 1 from the available pool of numbers.

Having solved the vertical equation for label 6, we now have the horizontal equation for label 7 as ? - 5 = 1. This can be rearranged as 5 + 1 = ? which gives the number 6 as the answer. This removes the number 6 from the pool of numbers available.

If you have done the easy equations first, those with just one missing number, you will have placed the numbers 1, 3, 6, 10, 15, 20 and 36.

Looking at the list of numbers available, there are no negative numbers which means that label 8 must be less than 10. There is no number 4 or 9 available and the numbers 1, 3 and 6 have already been placed. It cannot be the number 5 as there would need to be a second number 5 to make the equation work. It cannot be the number 7 as the number 3 has already been placed. So it is either numbers 2 or 8.

Assuming the label 2 number has been placed, it follows from the vertical equation through label 9 that label 10 is either the number 5 (i.e. 2 + 3) or 11 (i.e. 8 + 3). Since we have already worked out that label 5 is the number 36, the only number that works at label 10 is the number 11. This is because the horizontal equation through label 10 needs to have either the number 31 at label 11 (if label 10 is the number 5) or the number 25 (if label 10 is the number 11). Since there is no number 31, that means label 11 is the number 25. So that means label 8 is the number 2.

Having worked out that label 8 needs the number 2, we now have the equation (10 - 2 = ?). This means that the number 8 goes against label 9. This in turn makes finding the number for label 10 possible assuming you have found the number for label 1 and have then solved the horizontal label 2 equation.

Having worked out the numbers at labels 2 and 9, we now have the numbers for the equation to find the number for label 10. The equation is 8 + 3 = ? This gives us the number 11 to go against label 10.

The number for label 11 can be obtained through the horizontal equation once the numbers for labels 5 and 10 have been obtained. These are the numbers 36 and 11 respectively and results in the horizontal equation ? + 11 = 36. Subtracting 11 from 36 gives the number 25.

Having solved the earlier labels, there are four numbers left, namely 5, 7, 19 and 44. For label 15 we have the equation 24 - ? = ? As there are no negative numbers, we know that the number being subtracted from 24 is less than 24, so that rules out the number 44. It cannot be the number 7 as we would need 17 to complete the equation. So labels 12 and 15 are either the numbers 5 and 19 respectively or visa-versa.

We have worked out that the number for label 11 is 25. This means that the number 5 cannot be the one for label 12 as there is no number 30 to complete the vertical equation through label 12. This means that label 12 has the number 19.

We worked out that the number for label 11 from its horizontal equation, namely the number 25. We worked out that label 12 has the number 19. In the vertical equation ending in label 13, we can add the numbers 25 and 19 together to give the number 44 for label 13.

The equation for label 13 needs to be completed before this one can be calculated. With the number 44 at label 13, the horizontal equation including label 14 becomes ? + 44 = 51. Subtract 44 from 51 and the number for label 14 is revealed to be 7.

The final number can be obtained by solving the horizontal equation ending in label 15. We worked out earlier that label 12 was the number 19 so the equation is 24 - 19 = ? This gives the answer as the number 5. If you have followed the labelling sequentially to solve this puzzle so far, there should only be one number left, namely the number 5.