# The Ants Go Marching

**Number Theory**Level 3

The ants go marching one by one, hurrah hurrah

The ants go marching one by one

They march and one says he is done

The ants go marching, hurrah hurrah

The ants go marching two by two, hurrah hurrah

The ants go marching two by two, hurrah hurrah

The ants go marching two by two

They march and one gets crushed by a shoe

The ants go marching, hurrah hurrah

\(\vdots\)

The ants go marching ten by ten, hurrah hurrah

The ants go marching ten by ten, hurrah hurrah

The ants go marching ten by ten

They march and one gets eaten by a hen

The ants go marching, hurrah hurrah

The ants start walking in one row, lose a member, and then start walking in two rows. This continues, with them losing a member before increasing the number of rows, until they are walking in ten rows. If every time they walk in a new amount of rows, the number of ants per row of the marching contingent is still equal, what is the **least number of ants they could have started out with**?

i.e They may have started with 5 ants in one row and then 4 ants in two rows (2 ants per row) and then 3 ants in three rows (1 ant per row) and then it doesn't work anymore (can't evenly split 2 ants between four rows).

**Your answer seems reasonable.**Find out if you're right!

**That seems reasonable.**Find out if you're right!

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