The following are six sentences in Vietnamese and their translations to English in arbitrary order.

We can notice certain similarity in pronunciation between English and Danish numerals which might help us to solve the puzzle (but we are not going to use this fact). Let's also notice that there are several types of numerals: (1) fem, fir, seks, and ni - most likely present single-digit numbers; (2) more complicated numbers are formed with the help of tyve (as in femotyve, fireotyve, and niotyve) and den (as in niden, femden and treden); and (3) even more complicated numbers are formed with sins (such as firsinstyve) and hal (as in halvfemsinstyve).

1. From equation 2, fem times fem must have fem in the result of the multiplication. So fem can be either 5 (5x5=25) or 6 (6x6=36). In this case tyve will be either 20 or 30. The way how tyve is used seems to be similar to how twenty-five and thirty-five are formed in English, with the difference that the last digit is coming first. So femotyve could mean [5 and 20] or just 25.

2. Considering equation 1 (fem x fir = tyve), we have two options: fem = 5, tyve = 20, fir = 4 and fem = 6, tyve = 30, fir = 5.

At this point letâ€™s assume that tyve is 20 and den is 10, so femotyve = 25, femden = 15, fireotyve = 24, and so on. If this assumption is false then we will have to come back to this step and start over.

3. This is the most nontrivial step in the solution. We have to find out what sins stands for. Let's consider equation 5 (femden + femotresinstyve = firsinstyve). After trying different options and playing around with math, there is an unavoidable conclusion that sinstyve should mean how many times we take 20-ies to form the number, so sins is a connection particle. In this case, firsinstyve means 4 of 20-ies or simply four twenties. In English, for example, we can say four-hundred (4 of 100) for 400 and fifteen-hundred (15 of 100) for 1,500. The numeral system based on twenty is not that rare or unique, for example, it used in French.

4. If we accept the above assumptions then equations 5 makes perfect sense, in this case tre should mean 3: [5 and 10] + [5 and (3x20)] = [4 times 20] or 15 + 65 = 80.

The same is true for equation 4 (seks must be 6 and ni must be 9): [6 and (3 times 20)] + [9 and 10] = [5 and (4 times 20)] or simply 66 + 19 = 85.

5. The left side of equation 3 would translate then as: 84 + 6 and the right side of the same equation (halvfemsinstyve) should then translate as 90 or, in this case, 100 without 10 (5 times 20 without 10). We observed an interesting complication: since 90 can not be presented as an integer number of 20-ies we have to use 100 without 10. Similar 70 could be written as halfirsinstyve (70 = 80 - 10) and 50 as haltresinstyve (50 = 60 - 10).

6. Now it is not hard to fill in the blanks. The missing numbers are 16 (seksden), 54 (fireohaltresinstyve), and 93 (treohalfemsinstyve).