SOLUTION TO LAST MONTH'S QUIZ
1) 1, 2, 3
2) (i) 8 cubes have just three painted faces
(ii) 36 cubes have just two painted faces
(iii) 54 cubes have just one painted face
3) 421052631578947368
Notes
1). 1 + 2 + 3 = 6
1 X 2 X 3 = 6
This is the only solution involving positive whole
numbers. (If fractional values are allowed then two
of them can be assigned arbitrarily, and the third
easily calculated. For example: 3, 4, 7/11 )
2). As a check: Number of unpainted cubes = 27.
Then adding, 8 + 36 + 54 + 27 = 125, as expected.
3). Consider the unknown multiplicand ending in 8.
Multiply it by 2 with short multiplication, and
immediately copy each digit of the product into
the multiplicand. The process ends when 8 is
obtained without a corresponding carry digit.
