[ Arithmetic operations. Numerical identities]

Using five threes, arithmetic operations, and exponentiation, form the numbers from 1 to 10.

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First solution:

$1=(3: 3)^{333}$,

$2=(3-3: 3) \times 3: 3$,

$3=3 \times(3: 3) \times(3: 3)$

$4=(3+3: 3) \times(3: 3)$

$5=3+3: 3+3: 3$

$6=(3+3) \times(3: 3)^{3}$,

$7=(3+3)+(3: 3)^{3}$,

$8=(3 \cdot 3)-(3: 3)^{3}$

$9=(3 \cdot 3) \times(3: 3)^{3}$,

$10=(3 \cdot 3)+(3: 3)^{3}$

Second solution.

$1=(3 \times 3+3): 3-3$

$2=(3+3+3-3): 3$

$3=(3 \times 3+3-3): 3$

$4=(3+3+3+3): 3$

$5=(3 \times 3+3+3): 3$

$6=3 \times 3+3-3-3$

$7=3: 3+(3 \times 3-3)$

$8=(3 \times 3 \times 3-3): 3$,

$9=3+3+3+3-3$

$10=3: 3+3+3+3$

(Solution by 7th grade students of the "Traditional Gymnasium" in Moscow)

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