Mini militia

Probability Level 3

2310 troops are arranged in rows and columns such that each column has the same number of troops for a particular arrangement. how many arrangements are possible?


The answer is 32.

Deepansh Jindal by Deepansh Jindal , 19, India

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2 solutions

Zee Ell
Aug 7, 2016

2310 = 2 1 × 3 1 × 5 1 × 7 1 × 1 1 1 2310 = 2^1 × 3^1 × 5^1 × 7^1 × 11^1

ϕ ( 2310 ) = ( 1 + 1 ) 5 = 32 \phi (2310) = (1+1)^5 = 32 ,

meaning, that 2310 has 32 divisors.

Therefore we can choose the length of the (number of soldiers standing in a) row 32 \boxed {32} ways (which determines the length of the column and the arrangement as well).

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Achal Jain
Aug 8, 2016

Nice problem Deep

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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