Esteemed reader: Appended to problem 42 is a dialogue highlighting an unsettling outcome of a limited (and limiting) approach to mathematics education.

2015-02-26

219. Digital computing

★★★

To a three-digit integer A, in which the hundreds digit differs from the tens digit, apply the following operation:

OPERATION 
  
  The difference between the hundreds digit and tens digit of A becomes the digit in the hundreds place of a new three-digit integer, the difference between the tens digit and the ones digit of A becomes the digit in the tens place, and the difference between the hundreds digit and the ones digit of A becomes the digit in the ones place.  
  

⟦A⟧ is the notation for this operation.
For example, ⟦305⟧ = 352, ⟦737⟧ = 440.


There is only one integer A that meets all of the following conditions ①,② and ③. Determine integer A.

①  A is less than ⟦A⟧.
②  The difference between the hundreds digit of A and the hundreds digit of ⟦A⟧ is 1.
③  The difference between A and ⟦A⟧ is a one-digit integer.

(from Twitter)

2015-02-25

218. Square paper folding



In the diagram, ABCD is a square coloured paper.  Side CD is folded over so that the edge overlaps diagonal AC, forming crease CP, and point D goes to point D'.  Then side AB is folded over so that the edge overlaps point D', forming crease BQ, and point A goes to point A'.  Determine the number of degrees of both ∠x and ∠y.

2015-02-19

217. Comparing means


There are five numbers: A, B, 8, 13, and 20.

⒜  If the mean (average) of A and 8 equals the mean of B and 20, determine the difference of A and B.
⒝* If the mean of A, B, and 13 is one more than the mean of A and B, determine the mean of A and B.