Saving Ice-Cubes Base 4/3
Suppose that for every 4 ice-cubes, we will take out 3, put them in another glass and leave the 4th one to melt. Any remaining ice-cubes will be put back into the freezer. We will repeat this and any ice-cubes left will be sent back into the freezer. If we have 19 ice-cubes, how many will be sent back into the freezer?
The answer is 9.
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1 solution
For 16 of them, 4 will melt, 3 × 4 = 1 2 will be put into another glass and the remaining 3 will be sent back into the freezer. Let's use this as a digit in base 4/3
From the 12 we have, 3 will melt, 9 will be in another glass and no cubes will be sent back into the freezer. Record this digit as 0.
From the 9 we have, 2 will melt, 6 will be in another glass and 1 will be sent back in to the freezer. Record this digit as 1.
From the 6 we have, 1 will melt, 3 will be put in another glass and 2 will be sent back into the freezer. Record this digit as 2.
The last 3 cubes is less than 4. Put them back into the freezer. The number of cubes sent back into the freezer is the sum of the digits 32103