# To form!

I have a box full of lead soldiers with whom I play very often. They come from a box of 100 that they gave me some time ago although I have already lost some.

Today I am going to organize a parade with all of them so I take them out of the box and put them in formation six by six. When I am finishing placing them I see that I am missing five soldiers to complete the last line so I decide to do the training of five.

Again, when I have finished it, I see that I am missing 4 soldiers in the last line so I decide to try with a formation of 4 rows but at the end I see that I am again missing soldiers, specifically 3, so a bit annoying I restructure the army to make a three-row formation.

At the end I see that I am missing two soldiers to complete the last line of training so, angry, I decide to try a two-row formation and at the end I also see that I am missing a soldier, so I kick the soldiers and I I'm going for a bike ride.

Do you know how many lead soldiers I have?

#### Solution

We have to find a number X less than 100 such that divided by 2 days of remainder 1 that is X+1 is divisible by 2. By dividing it by 3 days of remainder 2, then X+1 is divisible by 3 and following the reasoning, X+1 is divisible by 4, 5 and 6. The least common multiple of 2, 3, 4, 5 and 6 is 60 so X + 1 = 60 and therefore I have 59 lead soldiers.