Puzzle for April 6, 2021 ( )
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
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Hint #1
Add D to both sides of eq.2: B + D + D = E – D + D which becomes B + 2×D = E In eq.4, replace E with B + 2×D: B + 2×D – A = A + B In the equation above, subtract B from each side, and add A to each side: B + 2×D – A – B + A = A + B – B + A which becomes 2×D = 2×A Divide both sides by 2: 2×D ÷ 2 = 2×A ÷ 2 which makes D = A
Hint #2
In eq.5, replace D with A: A × A = A + A which means A² = 2×A Divide both sides of the equation above by A: A² ÷ A = 2×A ÷ A which makes A = 2 which also makes D = A = 2
Hint #3
In eq.1, substitute A for D: C + A = A + F Subtract A from both sides of the above equation: C + A – A = A + F – A which makes C = F
Hint #4
Substitute C for F, and 2 for D in eq.6: C ÷ C = B – 2 which becomes 1 = B – 2 Add 2 to both sides of the equation above: 1 + 2 = B – 2 + 2 which makes 3 = B
Hint #5
Substitute 3 for B, and 2 for D in eq.2: 3 + 2 = E – 2 which makes 5 = E – 2 Add 2 to both sides of the above equation: 5 + 2 = E – 2 + 2 which makes 7 = E
Solution
Substitute 2 for D, and 7 for E in eq.3: 2 + 7 = F which makes 9 = F and also makes C = F = 9 and ABCDEF = 239279