• # Can anybody solve this problem?

After seeing the thread related to numbers and mathematics from Sarojah, I also got inspired and thought I can place this simple mathematical problem.

There is a water pond in a park. In that water pond, there are some lotus leaves. Some honey bees came there and want to rest on those lotus leaves. If one bee rest on each leaf, there will be no leaf left for one bee. If two honey bees rest on every leaf, one leaf will be left without any honey bee. I like to know the total number of honey bees that came and how many lotus leaves are there in the pond.

I think this simple mathematical question can be answered by many of our learned members.
• Very nice. iam just recalling my childhood memories. answer is 3 leaves and 4 honeybees.
shasthranaam Ganitham moordhanisthitham

• True. These riddles will be told in our childhood days only. My grandfather used to give such puzzles to me. For children, these are very interesting and make them think.
drrao
always confident

• Such problems are generally solved using algebra.
The two conditions mentioned in the question can be represented in algebraic form as under, where L is the number of lotus leaves and B is the number of bees -
L + 1 = B
2(L - 1) = B
Solving we get L = 3, and B = 4

Knowledge is power.

• I can provide another ways of solving this...

Let's assume there are 'n' lotus leaves in the pond.
According to the problem statement, if one bee rests on each leaf, there will be no leaf left for one bee. Therefore, we can say that the total number of bees is (n-1).

Also, if two honey bees rest on every leaf, one leaf will be left without any honey bee. Therefore, the number of lotus leaves should be such that it is one more than a multiple of 2.

So, let's try to find such a number:
2 x 1 + 1 = 3 (not divisible by 2)
2 x 2 + 1 = 5 (not divisible by 2)
2 x 3 + 1 = 7 (not divisible by 2)
2 x 4 + 1 = 9 (not divisible by 2)
2 x 5 + 1 = 11 (not divisible by 2)
2 x 6 + 1 = 13 (not divisible by 2)
2 x 7 + 1 = 15 (divisible by 2)

So, there are 15 lotus leaves in the pond.

If two bees rest on each leaf, then the total number of bees needed is:
2 x 15 = 30

However, according to the problem statement, there are only (15-1) = 14 bees. Therefore, one bee needs to rest on a leaf with 3 bees. This means that there are 3 lotus leaves and 4 honey bees in the pond.

Hence, the answer is 3 lotus leaves and 4 honey bees.

Learn one more language and you will feed your brain the top nutrition!
- Geeta

• Generally, such problems will be using algebra only. We have two unknown parameters but we know two relations between the two. By making two equations as mentioned by Umesh, solving the question will be easy,
The method suggested by Geeta is also another approach but a little more time is consumed.

drrao
always confident