Question

1.

- I am a multiple of 3
- I am an odd number
- the sum of my digits is 6
- my ones is one more than my tens digit
- my hundreds digit is 5 times my one digit
what number am I?

2.
- all my digits are different
-my ones digit is 4 times my hundreds digit
- my thousands digit is a perfect square
-my ones digit is 3 more than my tens digit
what number am I?

Answer 1

1. 501

2. 1258 or 4258 or 9258

Explanation:

1. represent number (d3d2d1) in terms of x. let x = 10's digit (dxd) then

d2 = x

d1 = x + 1

d3 = 5(x + 1) = 5x + 5

d3 + d2 + d1 = 6

(5x + 5) + (x) + (x + 1) = 6

7x + 6 = 6

7x = 0

x = 0 SO

d3 = (5x + 5) = 5

d2 = 0

d1 = x + 1 = 1

501

2. d4d3d2d1 and d1 not = d2 not = d3 not = d4, let d3 = x and d2 = y then

d2 = y

d3 = x

d1 = 4x and d1 = y + 3 so 4x = y + 3 or y = 4x - 3

d4 = perfect square (1 or 4 or 9)

any d must be <= 9

d4d3d2d1 = (1 or 4 or 9)(x)(4x - 3))(4x) so x<3 (0,1,2) or d1 fails <= 9

(1,4,9)(0,1,2)((4x - 3 = (1,5))((4x = 0,4,8)

d3 (0,1,2) must be 2 because 0 does not work for d2 and 1 does not work for d1, so this make d1 (4x) = 8 so

(d4)(2)(4x - 3 = 5)(4x = 8) = d4 (1,4,9) and 258 so

1258 or 4258 or 9258