It's just a rearrangement of numbers

Number Theory Level 1

1 × 3 × 5 × 7 × 9 × 2 5 × 5 ! = x ! , x = ? \large 1 \times 3 \times 5 \times 7 \times 9 \times 2^5 \times 5! = x! \quad, \quad x = \ ?


The answer is 10.

Rawan Medhat by Rawan Medhat , 22, Egypt

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1 solution

Rearranging the terms on the left hand side we see that it can be written as 1 ⋅ 5 ! ⋅ 2 ⋅ 3 ⋅ 7 ⋅ 2 3 ⋅ 9 ⋅ 2 ⋅ 5. 1\cdot 5!\cdot 2\cdot 3\cdot 7\cdot 2^{3}\cdot 9\cdot 2\cdot 5. This is 1 ⋅ 5 ! ⋅ 6 ⋅ 7 ⋅ 8 ⋅ 9 ⋅ 10 , 1\cdot 5!\cdot 6\cdot 7\cdot 8\cdot 9\cdot 10, which is 10!. This is the answer we were looking for.

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