How many of rulers do you need to make a measurement of 1CM?
Number Theory
Level
4
We have an infinite amount of rulers with no markings on them. We only know that they measure either 587 cm or 13 cm respectively.
How many rulers of 13 cm do we need at least in order to measure 1 cm?
The answer is 271.
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13 × 45 = 585. We can use this to measure 2 cm with the help of the 587 ruler.
Repeating this 6 times will give us 12 cms. Then we need just one more 13 ruler to get 1 cm. Thus the answer is 45×6+1=271