Question

A broken clover has 2 leaves, a normal clover has 3 leaves and a lucky clover has 4 leaves. In a bunch of these clovers , there are twice as many normal clovers as broken clovers and 5 times as many normal clovers as lucky clovers. The bunch has a total of N leaves. N is greater than 200. What is the lowest value of N?

Answer 1

n = 2b
n = 5l
2b+3n+4l > 200

2(n/2) + 3n + 4(n/5) > 200
n + 3n + 4n/5 > 200
24n/5 > 200
24n > 1000
n > 41.666
n >= 42
b >= 21
l >= 9
2*21 + 3*42 + 4*9 = 42 + 126 + 36 = 204

So, N >= 204 leaves in total

Answer 2

Actually n=5l, so n=42 and l=9 does not work.

Answer 3

For a base unit of clovers, there would be 10 normals, 5 brokens, and 2 luckies. so 10 normals = 30 leaves, 5 brokens = 10 leaves, and 2 luckies = 8 leaves. So 48 leaves in a base unit. So basically what is the first multiple of 48 that is greater than 200. 240 is the answer. Guo out. Brian says hi

Answer 4

Guys its
E Strategy: Determine the possible numbers of normal leaves.
The number of normal clovers is a multiple of 5, since there are 5 times as many normal
clovers as lucky clovers. The number of normal clovers is also even, since there are twice
as many of them as there are of broken clovers. The number of normal clovers is therefore
a multiple of 10.
For each 10 normal clovers, there are 2 lucky clovers and 5 broken clovers.
Split the collection of N clovers into groups so that each group has 10 normals, 2 luckies,
and 5 brokens. The number of leaves in each group is 10×3 + 2×4 +5×2 = 48.
The total number of leaves is a multiple of 48, and the least multiple of 48 that is greater than
200 is 5×48 = 240. The least value of N is 240.