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April 19, 2014

April 19, 2014

Posted by **Anonymous** on Wednesday, April 18, 2012 at 12:00am.

- math -
**Anonymous**, Tuesday, May 8, 2012 at 3:55amplease help me too

- math -
**DHNWAC**, Monday, May 21, 2012 at 5:26amWe must assume that the centre of the tile is perfectly centered on a square on the number chart, and that the chart is big enough for all of the tile to stay within the borders of the chart.

If this is the case it can be proven in the following way:

Let the number covered by the centre be denoted x. Let y < x be any other number on the chart covered by the cross tile. We may write y = x-k for some natural number k.

Due to symmetry y' = x+k will be covered on the chart as well. Since the tile only covers pairs (x-k,x+k) and each pair has x as average the average of all numbers covered will be x. This could be explained in a little more detail but I hope this suffices as it gets lengthy otherwise!

- math -
**DHNWAC**, Monday, May 21, 2012 at 5:26amWe must assume that the centre of the tile is perfectly centered on a square on the number chart, and that the chart is big enough for all of the tile to stay within the borders of the chart.

If this is the case it can be proven in the following way:

Let the number covered by the centre be denoted x. Let y < x be any other number on the chart covered by the cross tile. We may write y = x-k for some natural number k.

Due to symmetry y' = x+k will be covered on the chart as well. Since the tile only covers pairs (x-k,x+k) and each pair has x as average the average of all numbers covered will be x. This could be explained in a little more detail but I hope this suffices as it gets lengthy otherwise!

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