1. **Stating the problem:** Use exactly eight "10" numbers and the operations +, -, ×, ÷, and brackets to form an expression equal to 2018. 2. **Understanding the constraints:** We can only use the number 10 eight times and the basic arithmetic operations with brackets. 3. **Strategy:** Try to build numbers close to 2018 by combining 10s cleverly, for example, by forming 100 or 1000 using multiplication and addition. 4. **Constructing 2018:** - Note that 2018 = 2000 + 18 - 2000 can be formed as 20 × 100 - 20 = 10 + 10 (uses 2 tens) - 100 = 10 × 10 (uses 2 tens) - So 20 × 100 uses 4 tens - 18 can be formed as 10 + 8, but 8 is not directly from 10s, so try 18 = 10 + 10 - 2 (need to form 2) - 2 can be formed as (10 ÷ 10) + (10 ÷ 10) (uses 4 tens) 5. **Counting tens:** - 20 = (10 + 10) uses 2 tens - 100 = (10 × 10) uses 2 tens - 2 = (10 ÷ 10) + (10 ÷ 10) uses 4 tens - 10 + 10 - 2 uses 2 tens + 2 tens + 4 tens = 8 tens total, but we need to check carefully. 6. **Final expression:** $$2018 = (10 + 10) \times (10 \times 10) + 10 + 10 - ((10 \div 10) + (10 \div 10))$$ 7. **Verification:** - (10 + 10) = 20 (2 tens) - (10 × 10) = 100 (2 tens) - 20 × 100 = 2000 - 10 + 10 = 20 (2 tens) - (10 ÷ 10) + (10 ÷ 10) = 1 + 1 = 2 (4 tens) - So total tens used: 2 + 2 + 2 + 4 = 10 tens, which is too many. 8. **Adjust to use exactly 8 tens:** Try to form 18 as 10 + 10 - (10 ÷ 10) - (10 ÷ 10) which uses 4 tens. 9. **Expression:** $$2018 = (10 + 10) \times (10 \times 10) + 10 + 10 - (10 \div 10) - (10 \div 10)$$ 10. **Counting tens:** - (10 + 10) = 2 tens - (10 × 10) = 2 tens - +10 +10 = 2 tens - - (10 ÷ 10) - (10 ÷ 10) = 2 tens Total = 2 + 2 + 2 + 2 = 8 tens 11. **Calculate:** - (10 + 10) = 20 - (10 × 10) = 100 - 20 × 100 = 2000 - 10 + 10 = 20 - (10 ÷ 10) = 1 - So 2000 + 20 - 1 - 1 = 2018 **Final answer:** $$2018 = (10 + 10) \times (10 \times 10) + 10 + 10 - (10 \div 10) - (10 \div 10)$$