You are to find expressions for each whole number from 1 through 20, using in each expression exactly four 4�s, plus any mathematical symbols you like: parentheses, plus signs, etc.
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4 + 4 |
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| 4 + 4 |
Show/Hide Solution
There are many possibilities. Here are some:
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11 = 4 + 4 + 4 – [√√4]
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13 = 4 + 4 + 4 + [√√4]
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4 = √4 + 4 + 4 + 4
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| 8 = √4 + √4 + √4 + √4 |
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19 = 4 · 4 + √4 + [√√4]
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Note: [] is the greatest integer function. That is, [x] is the greatest integer less than or equal to x.
For example, [√√4] = [√2] ≈ [1.4] = 1.