Various sets of numbers add together to give a sum of 100:

• $30 + 70 = 100$
• $20 + 80 = 100$
• $21 + 56 + 23 = 100$
• $10 + 10 + 10 + 10 + 10 + 10 + 20 + 20 = 100$

The products of these sets are all different:

• $30 \times70 = 2100$
• $20 \times 80 = 1600$
• $21 \times 56 \times23 = 27048$
• $10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 20 \times 20 = 400000000$

What is the greatest product that can be made from whole numbers that add up to 100?

Try using different starting numbers.

Can you find a strategy for splitting numbers so that you always get the largest product?