Shaggy has to learn the same 71 hiragana characters, and also has one week to do so; unlike Velma, he can learn as many per day as he wants. However, Shaggy has decided to obey the advice of a study-skills professional, who has advised him that the number of characters he learns on any one day should be within 4 off the number he learns on any other day.
(A) What is the least number of hiragana that Shaggy could have to learn on Saturday?
(B) What is the greatest number of hiragana that Shaggy could have to learn on Saturday?
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palvarez
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min, all others max.
s, s+4
s + 6(s+4) = 71
7s = 47
s = 6 5/7
Pick the ceiling of that integer, so that ceiling(s+4) gets maximized.
floor(6 5/7) = 7
7, 11,11,11,11,10,10,
2. max, all others min
s, s-4
s+6(s-4) = 71
7s = 95
s =13 4/7
pick the floor of s, since floor(s-4) gets minimized.
13, 10, 10,10,10,9,9
s, s+4
s + 6(s+4) = 71
7s = 47
s = 6 5/7
Pick the ceiling of that integer, so that ceiling(s+4) gets maximized.
floor(6 5/7) = 7
7, 11,11,11,11,10,10,
2. max, all others min
s, s-4
s+6(s-4) = 71
7s = 95
s =13 4/7
pick the floor of s, since floor(s-4) gets minimized.
13, 10, 10,10,10,9,9
