Mental-Math kata - Make 11 from five digits

Sep 6, 2023 | Dundas

Mental Math Kata

By Mathnasium of Dundas | Added Sep. 1, 2023

Martial arts practitioners have a long tradition of daily kata, to keep their skills sharp. Those of us who would keep our mental math skiils sharp should do so also. Heres a fun one I play with license plate numbers as I drive, whenever a five digit plate comes into view:

Make 11, using all five digits (so no leaving any out) and these seven basic arithmetic operations:

  • +   (Addition);
  • −   (Subtraction);
  • ×   (Multiplication);
  • ÷   (Division);
  • ( ... ) Parentheses
  • ‾‾ (Square Root); and
  •   (Square)

What's that last one you ask? It's just how my Dad, who taught me the game, learned to write squaring in Schiedam in the 1930's. Ultimately, it makes the exercise more fun by increasing possibilities for a solution.

Of course, we don't need to be in the car to try this. Let's practice with five of a single digit to start:

  1. Five 9's: so {9, 9, 9, 9, 9}
    9 + ( 9 ÷ 9 ) + ( 9 ÷ 9 )
    = 9 + 1 + 1
    = 11
    Done; using all five 9's just as required.
    That wasn't too hard. Let's try another.

  2. Five 1's: so {1, 1, 1, 1, 1}
    (1 + 1 + 1) + 1 + 1
    = 3 + 2
    = 9 + 2
    = 11
    A bit trickier; but again completed.

Try some more choices for a digit repeated five times; or dig out the D&D 10-sided dice and get a random selection. Of the single digits repeated five times, 7 is likely the most challenging, so leave it until last. If rolling dice generates too many 0's, add the factorial operation (!) to convert those pesky 0's into 1's.


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Students! This Saturday, September 9 (and again October 7) we are hosting Kids' Corner at the Waterdown Farmers' Market, in the Legion parking lot.

  • Drop by to say "Hello." - and earn a full card.
  • Introduce us to a friend, from 8 to 18 - and earn a second full card.

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