Puzzle for November 4, 2019 ( )
Scratchpad
Find the 6-digit number ABCDEF by solving the following equations:
A, B, C, D, E, and F each represent a one-digit positive integer.
Scratchpad
Help Area
Hint #1
In eq.3, replace D with B – C (from eq.5): B = B – C + E In the equation above, add C to both sides, and subtract B from both sides: B + C – B = B – C + E + C – B which makes C = E
Hint #2
In eq.4, replace E with C: C + C = D which means 2×C = D
Hint #3
In eq.5, substitute 2×C for D: 2×C = B – C Add C to both sides of the above equation: 2×C + C = B – C + C which makes 3×C = B
Hint #4
Substitute C for E, and 3×C for B in eq.2: C + F = 3×C + C which becomes C + F = 4×C Subtract C from each side of the above equation: C + F – C = 4×C – C which makes F = 3×C
Hint #5
Substitute 3×C for F in eq.6: 3×C ÷ C = E which means 3 = E making C = E = 3 B = F = 3×C = 3 × 3 = 9 D = 2×C = 2 × 3 = 6
Solution
Substitute 9 for B and F, 3 for C for E, and 6 for D in eq.1: A + 9 + 3 + 6 + 3 + 9 = 34 which simplifies to A + 30 = 34 Subtract 30 from each side of the equation above: A + 30 – 30 = 34 – 30 A = 4 and ABCDEF = 493639