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英国人杜德(1857—1931)曾经指出:一根长13厘米的尺子,只须刻上四个刻度(刻在1、4、5、11厘米处),便可一次量出1～13厘米之间任何整厘米数的长度。第二届“华罗庚金杯”少年数学邀请赛决赛面试(中学组)第7题是:有一把长为9厘米的直尺。你能不能在上面只刻上三条刻度线,使得这把直尺可以量出从1至9厘米的所有整厘米长度? 这类“有刻度尺子问题”的一般情形是: 有一把长为m厘米的直尺,问最少要设置多少刻度,才能使这把直尺可以一次量出从1至m厘米的所有整厘米长度?
The Englishman Dodd (1857-1931) once pointed out that a ruler with a length of 13 centimeters only needs to be engraved with four scales (inscribed at 1, 4, 5, and 11 centimeters), and it can measure 1 to 13 centimeters at a time. The length between any whole centimeters. The seventh question of the second “Hua Luogeng Gold Cup” Junior Math Invitational Interview (Secondary School Group) is: There is a ruler with a length of 9 cm. Can you just engrave the three tick marks above so that the ruler can measure all full centimeters from 1 to 9 centimeters? The general situation for this type of “scaled ruler problem” is: There is a length of m cm. The ruler, asked how many scales to set at least, in order to make this ruler can measure all the entire cm length from 1 to m cm at a time?