One, four
Pierino collects his savings in a box. When his father opens the box, he adds , when his grandfather opens the box he adds times the content (in order to quadruplicate it). Before Pierino goes to the campsite there is just in the box, and when he finally comes home he finds .
How many times, at least, his father opened the box during his vacation?
The answer is 6.
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1 solution
406 (base 4) = 4 4 + 2 × 4 3 + 4 2 + 4 + 2 =((((4×1+1+1)×4+1)×4+1)×4+1+1: six times ok. It's the minimum? Yes because 406 is not multiple of four: the previous step is "+1". So the previous. We can obtain 404 with "x4". If not we make almost 4 step "+1". Sorry for language