Question

How many numbers can you make between 0-99 using exactly four 4s and the operations $$ +,−,×,÷?

Answer 1

Answer:

  37

Step-by-step explanation:

I find 37 numbers in that range:

  {0, 1/16, 1/8, 1/5, 1/3, 1/2, 3/4, 4/5, 1, 5/4, 4/3, 2, 3, 7/2, 15/4, 4, 17/4, 9/2, 5, 6, 7, 8, 9, 12, 15, 16, 17, 20, 24, 28, 32, 36, 48, 60, 64, 68, 80}

For these numbers we have used only the indicated operations. No minus signs were used.

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Additional comment

Of the 320 ways the numbers can be combined, 15 result in division by zero. Many other results are outside the 0-99 range of interest. In total, there are 56 unique rational results.