First of all the answer was yes, you can fit the 70 cm sword. I'll congratulate the winners on Facebook but for now the solution. The box was 30cm X 40cm X 50cm. We will solve by a repeated use of the Pythagorean theorem. First the bottom:
30 squared + 40 squared = hyp squared
900 + 1600 = 2500 --> hyp = 50
Use this in a second application of the Pythagorean theorem:
50 squared + 50 Squared = large hyp squared
2500 + 2500 = 5000 --> hyp = 70.5cm THE SWORD WILL FIT YAY!!!!!
Now the first two answers (the missing integers)
As we recall we had some info regarding the product and sum of 5 one-digit integers (product = 2520, Sum = 30). We know two of the integers are 8 and 1. 5 must be one of the numbers since 2520 ends in 0. Subtracting from 30 we get 16. Which means we get 8 and 8 or 9 and 7, but the numbers must be different so 9 and 7 it is. Therefore the numbers are 1, 8, 9, 5 , 7.
If we allow the numbers to be the same the only other choice is 8 and 8 BUT the product is not 2520 so the answer to the adjunct problem is that we get no additional answers.
1, 8, 9, 5, 7 are the only solutions.