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The Fifty Force Field
Square any number from 41 to 59 in two quick steps. Spot the pattern first. The rule comes after you have found it yourself.
Look at these six squares
Look at the last two digits of every answer: 09, 04, 01, 01, 04, 09. Where have you seen these numbers before?
Now look at the first two digits
They go 22, 23, 24, then 26, 27, 28. Every answer circles around 25. Compare the gold digits with how far each number is from 50.
You found the rule
Find how far the number is from 50. Step 25 up or down by that distance for the first two digits. Then write the distance squared as two digits.
A 50 by 50 square has too many tiles to count, so here is the same idea on a 10 by 10 square, to find 72 = 49. Take away three columns down the right side and three rows along the bottom.
The whole square is 10 × 10 = 100 tiles. The three columns hold 3 × 10 = 30 tiles, and the three rows hold another 30. The little 3 by 3 corner belongs to both, so we took it away twice and must put its 9 tiles back once:
Now 472. It is the very same picture, just bigger. Start with a 50 by 50 square.
take off 3 columns of 50: 2500 − 150 = 2350
take off 3 rows of 50: 2350 − 150 = 2200
put the 3 × 3 corner back: 2200 + 9 = 2209
The 100 × (25 ± d) part gives the first two digits. The d2 part fills the last two digits, which is why we always write it as two digits. For 53: 100 × 28 + 9 = 2809. For 47: 100 × 22 + 9 = 2209.
Eight questions, no calculator
Practice round done
Perform the Mind Reader
Now try it on someone at home. Ask them to secretly pick a number from 41 to 59, square it on a calculator and tell you only the answer. Look at the last two digits for the distance, and the front for the direction. Then tell them the number they picked.
Most people cannot work backwards from a square at all. Doing it in your head looks impossible, which is exactly what makes it a good trick to perform.