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Standard Index Form Matching

Age 14 to 16 Challenge Level:

The questions posed were:

  • How do you know that two cards match?
  • Are some pairs easier to match than others?
  • Can you create some more cards to add to the sets?

We received the following solution from Mahdi from Mahatma Gandhi International School in India. The strategy Mahdi describes is a strategy for matching the cards very quickly, once you are already confident of whether two cards match and once you already know which pairs you find easier/more difficult to match. We are still open to receiving solutions which address these questions.

Mahdi's solution:
The key strategy here I used was to boil down the possibilities every time two cards matched. Throughout the games, I observed that half of the card is simplified and half weren’t. Thus over time, I started to take the hardest one (not- simplified ) and simplify that using the powers of 10. Mainly I did this but also started to find some connection between the numbers in the numerator and the denominator. So now I had simplified one card and approximated it in less than 3-4 seconds. Next, I looked for the simplified cards and tried to match the powers. There were most of the times two cards that had matching powers of 10, so I used the simplified numbers in division or multiplication (numerator and the denominator) to boil down that as well. So now I had a matching pair in less than 6-7 seconds. I continued doing this (starting to find hardest and matching it with one of the simplified ones) and quickly the possibilities of matching 10 powers reduce. Then  I could easily find the matching pairs by just approximating powers of 10. I did not have to be precise with division or multiplication. One key thing I had to remember was that sometimes the numbers in the numerator and denominator also changed the powers of 10, so I had to keep that in mind.