Puzzle for May 9, 2022 ( )
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Find the 6-digit number ABCDEF by solving the following equations:
A, B, C, D, E, and F each represent a one-digit non-negative integer.
Beginning today, and for each day of the upcoming week, we're featuring a puzzle sent to us by frequent contributor Judah S (age 15). Thanks for today's puzzle, Judah, and for every puzzle this week!
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Hint #1
Add E to both sides of eq.5: E + E = A – E + E which makes 2×E = A
Hint #2
In eq.1, replace A with 2×E: 2×E + E = B – E which becomes 3×E = B – E Add E to both sides of the above equation: 3×E + E = B – E + E which makes 4×E = B
Hint #3
In eq.6, replace A with 2×E, and B with 4×E: F = 2×E + 4×E which makes F = 6×E
Hint #4
In eq.4, substitute 6×E for F, and 4×E for B: D = 6×E – 4×E which makes D = 2×E
Hint #5
Substitute 2×E for D, and 6×E for F in eq.3: C = 2×E + 6×E which makes C = 8×E
Solution
Substitute 4×E for B, 8×E for C, and 2×E for D in eq.2: 4×E = 8×E ÷ 2×E which makes 4×E = 4 Divide both sides of the above equation by 4: 4×E ÷ 4 = 4 ÷ 4 which means E = 1 making F = 6×E = 6 × 1 = 6 B = 4×E = 4 × 1 = 4 C = 8×E = 8 × 1 = 8 D = 2×E = 2 × 1 = 2 F = 6×E = 6 × 1 = 6 and ABCDEF = 248216