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Largest Product

Stage: 3 and 4 Challenge Level: Challenge Level:1

Here are some different ways in which we can split 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 largest product that can be made from whole numbers that add up to 100?

Choose another starting number and split it in a variety of ways.
What is the largest product this time?

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


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