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Home » How Many Pennies Fit in One Roll? The Penny Puzzle You’ve Been Wrong About! - Carbonext

How Many Pennies Fit in One Roll? The Penny Puzzle You’ve Been Wrong About! - Carbonext

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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f(3) &= 27a + 9b + 3c + d = 5 \\
f(4) &= 64a + 16b + 4c + d = 11 \\
Subtract consecutive equations to eliminate $ d $:
$ (8a + 4b + 2c + d) - (a + b + c + d) = -1 - 3 \Rightarrow 7a + 3b +...
$ (27a + 9b + 3c + d) - (8a + 4b + 2c + d) = 5 + 1 \Rightarrow 19a + 5...
$ (64a + 16b + 4c + d) - (27a + 9b + 3c + d) = 11 - 5 \Rightarrow 37a...
Now subtract to eliminate $ c $:
Subtract: $ (9a + b) - (6a + b) = 0 - 5 \Rightarrow 3a = -5 \Rightarro...
Substitute into $ 6a + b = 5 $:
6(-\frac{5}{3}) + b = 5 \Rightarrow -10 + b = 5 \Rightarrow b = 15

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