A New Twist on Arranging Addends

Of all the original games I’ve designed, Arranging Addends is among my favorites. On page 1 of the Web Sketchpad model below (and here), you’re given five addends—1, 2, 4, 8, and 16—and asked to arrange them in the circles so that the sum of the numbers in each circle matches the values in the top-left corner of the page. You can drag both the numbers and the circles until all three sums are simultaneously correct (A short video at the end of this post demonstrates the mechanics of the game.)

There are an assortment of addends that can be used to give the game some variety, and below I list their values. These are mostly variations that I’ve shared before, but page 5 of the websketch introduces a new twist, suggested by Tom Francome. Now, the list of addends includes negative as well as positive values (1, –2, 4, –8, 16, –32, and 64) making this a particularly challenging variation to solve.

  • Page One: The addends are 1, 2, 4, 8, and 16 with sums between 1 and 31.
  • Page Two: The addends are 1, 2, 4, 8, 16, and 32 with sums between 1 and 63.
  • Page Three: The addends are 1, 2, 4, 8, 16, 32, and 64 with sums between 1 and 127.
  • Page Four: The addends are 1, 1, 3, 3, 9, 9, 27, and 27 with sums between 1 and 80.
  • Page Five: The addends are 1, –2, 4, –8, 16, –32, and 64 with sums between -42 and 85.
  • Page Six: Students create their own Arranging Addends puzzles.

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