Answer to this week's puzzles.

Dear Puzzlers,

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.