The puzzle of counting bees flying to their favorite flowers
If one-fifth of a hive of bees flew to the Lavender flowers, one-third flew to the Sunflowers, three times the difference of these two numbers flew to the Bee balm flowers, and two bees continued to fly around, unable to decide between the attractive fragrances of Hasnuhana and Ketaki, what was the number of bees in the hive? Use no algebra with any variable.
Time to solve: 3 minutes (not a stringent time limit).
How to proceed when habit of using conventional math urges you to form algebraic equations first? This is the challenge in solving this cute little confusing puzzle.
Solution to Counting the bees flying to favorite flowers puzzle
Solving in mind has the advantage of doing away with algebraic equations.
Basic math knowledge:
- Fractions are of the unknown total.
Just proceed with the fractions:
- First, the third group of bees: Three times the total of difference of one-third and one-fifth is: 3 x (1/3 -1/5) = 6/15 = 2/5.
- Two-fifth of total number of bees chose Bee balm flowers.
Bees flying to favorite flowers:
- Fraction of bees choosing their favorite flowers: (1/5 + 1/3 + 2/5) = 14/15.
So, the fraction of confused bees is just 1/15th of total number of bees.
Basic concept of a ratio fraction 1/15:
- The fraction has no units. It expresses the numerator as 1 portion out of total denominator of 15 portions.
No specific numbers, just PORTIONs of TOTAL.
Final step of solution by Unitary method:
- 1 of total 15 portions of bees were confused.
- If this one portion of confused bees are 2 in number, total number of bees of 15 portions is 15 x 2 = 30.
Most people are aware of these basic math concepts and methods and so, should solve the little puzzle without any difficulty.
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