Split the number 17 into whole numbers, multiply these numbers together. What is the highest number that can be made ?

Question

Working from left to right, calculate the numbers in the order shown (without using order of operation).

Replace each question mark with a mathematical sign. Plus, minus, multiply and divide can each be used once only.

What are the highest and lowest numbers that can possibly be scored?

9 ? 3 ? 4 ? 7 ? 5 =

Answer 1

486

---

we can split 17 in many ways as below
1. 17=1*17
2. 17=2*8+1 or better way 2*7+3
3. 17=3*5+2
4. 17=4*4+1 or better way 4*3+3+2 (as 3*2>5)
5. 17=5*3+2
6. 17=6*2+5 or better way 6*2+3+2
7. 17=7*2+3
8. 17=8*2+1 or better way 8+9
the max number we can get is 3^5*2=486