Mahaviracharya/Ganita Sara Samgraha/Chapter VI/219

Mahaviracharya: Ganita Sara Samgraha Chapter $\text {VI}$: Mixed Problems: Problem $219$

In how many ways can different numbers of flavours be used in combination together, being selected from:

the astringent

the bitter

the sour

the pungent

and the saline

together with the sweet taste?

Solution

$64$

Proof

A simple application of Cardinality of Power Set of Finite Set.

There are $6$ different flavours.

The number of different combinations is equal to the number of different subsets of this set of $6$.

Hence the number is:

$2^6 = 64$

$\blacksquare$

Sources

• c. 850: Mahaviracharya: Ganita Sara Samgraha: Chapter $\text {VI}$: Mixed Problems: $219$
• 1912: Rao Bahadur M. Rangacharya: The Ganita-Sara-Sangraha of Mahaviracharya: Chapter $\text {VI}$: Mixed Problems: $219$
• 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): Indian Puzzles: $51$