My smart 15-year-old high school girls
I have been fortunate enough to teach math to seven very smart girls.
The girls are so smart that they can add numbers without knowing those numbers.
If you want to know how the girls do that, you should read on.
To make this possible, the girls each have a yellow card. When all the girls have put that card away, they are ready. Because there are only 7 girls in the class the numbers added must be less than 128. With a larger class, it could well have been more.
How does it work? Very simple: the teacher comes up with a number, for example 6. He translates this number into a binary number: 0000110. The girls stand neatly side by side in front of the board. The teacher whispers a plus or a minus in each girl's ear. A plus if there is a 1 in the binary number at that girl's location and a minus otherwise. This way the girls can never know what the numbers are! They remember what was whispered in. Then the teacher does the same for the second number. Now the seven girls come into action. They apply the following five rules.
Rule 1
- minus × minus = plus
- minus × plus = minus
- plus × minus = minus
- plus × plus = plus
Rule 2
If a girl has heard at least one minus she puts away her yellow card. Each girl applies rule 1 and remembers the result (i.e. plus or minus). What the teacher has whispered they may forget. A girl may receive a card from another girl (see below).
Rule 3
If a student has another yellow card, she gives it to her right neighbor. She is free to decide when to do so. The neighbor considers the card as an additional whispered minus and thus applies rule 1 and remembers the result.
Rule 4
Girls who (after rule 3) turn a + into a − discard one yellow card.
Rule 5
When all the yellow cards have been put away then all the students who have finally memorized a minus raise their finger. The teacher considers each raised finger to be a binary 1 and no finger to be a binary 0. This creates a binary number, which is the sum of the two numbers the teacher had in mind. The girls added up the numbers for him!
If you don't believe this then you can play the simulation here.
Tip for when you do the simulation: take two "interesting" numbers, for example 27 and 26. But feel free to try 100 and 27 as well. You can see the result of 27 + 26 below.
