Shannon’s dad gave her a penny today to put in her new piggy bank. Tomorrow he will give another penny to make 2 pennies, and the next day he gives her 2 pennies to make 4 pennies. Each day he doubles the number of pennies from the day before.

After 16 days, Shannon’s bank is full.

On what day was Shannon’s bank half-full?

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Filed under: Today's Problem | Tagged: math, money, patterns |

Jon Manon, on November 25, 2008 at 2:13 pm said:This is an interesting twist on the usual doubling (exponential function) problem in that it m takes an easy problem (how many coins after 16 doublings) and tempts us to think in linear ways – e.g. we are tempted to say half of 16 or 8 days until we remember the exponential nature of the situation. Very nice. It makes me wonder whether the solution to this particular problem is easily generalizeable?

Tesh, on November 25, 2008 at 2:21 pm said:Nice. This reminds me of MindTrap, and is precisely the sort of question that I’ll be asking my children when I teach them math.

Jon, what precisely do you mean by generalizable? Condensed to a variable equation? Or perhaps just a “rule of thumb”?