data:image/png;base64,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 magic numbers will have to be computed instead when we add more inputs later.2data:image/png;base64,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's somewhat artificial that we start with shape inputs for DRAW BRICK but have fixed values in DRAW ROW A and DRAW ROW B. Acknowledge that if students bring it up. The main reason we did this is that DRAW ROW B is easier if they can do the arithmetic instead of building algebraic expressions for the general case.3. The reason that the obvious attempt (with exactly half-size bricks at the ends) fails is that a row B has an extra cement gap -- six of them instead of five. Since we're using a length of 4 for a cement gap, the two end bricks must be reduced by 4/2 = 2 steps each, that is, to 13 instead of 30/2 = 15.