7155
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2011-02-01T00:00:01
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<p>A grocer places some oranges, peaches, apples and bananas in a row so that, somewhere in the row each type of fruit can be found next to each other type of fruit. What is the smallest possible number of fruits in the row?<br></br>
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If you liked this problem, <a href="http://nrich.maths.org/6571&part=">here is an NRICH task</a> which challenges you to use similar mathematical ideas.</p>
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<p>Each fruit can have at most two fruits next to it but each type of fruit must be next to three other types of fruit so there are at least two of every fruit. This means there are at least $8$ fruits in total. In fact $8$ are sufficient, as shown in the arrangement<br></br>
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<span style="font-weight: bold;">OABPOBAP</span> (<span style="font-weight: bold;">O</span> for Orange, <span style="font-weight: bold;">P</span> for Peach, <span style="font-weight: bold;">A</span> for Apple, <span style="font-weight: bold;">B</span> for Banana)<br></br>
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Weekly Problem 8 - 2011
Weekly Problem 8 - 2011
Using, Applying and Reasoning about Mathematics
Working systematically
Using, Applying and Reasoning about Mathematics
Selecting and using information