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Largest Product

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

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?


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