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• # A Tough Sunday Morning Mathematics Puzzle

Long long back, I used to submit weekly puzzle on every Sunday. Today, I am submitting a mathematical puzzle. At the outset, I must warn that this is a tough puzzle and may consume lots of precious time on this Sunday morning.

Now, here is the puzzle:

In a mythical land, there are two kinds of apples: red apples and green apples. The red apples get doubled in quantity every day, and the green apples get tripled every day. On the first day, there are only one red apple and one green apple. After how many days will the total number of apples (both red and green apples combined) be exactly 793?

The first member giving the correct answer will get a virtual gift from me. I will provide the correct reply and explanation after, say, 24 hours.
• Red +green
1+1 = 1st day
2+3= 2nd day
4+9=3rd day
8+27=4th day
16+81=5th day
32+243=6th day
64+729=7th day is 793

shasthranaam Ganitham moordhanisthitham

• Let after n days the total of red and green apples become 793.
So -
2^n + 3^n = 793
It can be solved by trying n=1 and upwards to reach a solution at n = 7.
Sarojah has already done that in her response above.

Alternatively it can be solved by taking logarithm of both sides and then finding n.

Knowledge is power.

• The puzzle is solved by Sarojah very easily without any issues.
But the figure is only 793, we can get it in 7 days easily. Then we may have to use algebra equations as mentioned by Umesh and solve the puzzle. Whatever may be method we adopt the answer is 7 days.

drrao
always confident

• Sarojah Madam was the first member who gave the correct answer.

Umesh Sir provided the correct mathematical equation for the problem.

Dr. Rao Sir correctly stated that if the power of n is higher, then the puzzle would be very difficult to solve.

The virtual gift goes to Sarojah Madam.

(a) Those who have forgotten Noakhali, how can they protest Sandeshkhali?
(b) Have no fear of perfection - you'll never reach it. ---------- Salvador Dali

• Thank you Partha for your virtual gift. The method I adopt also the same what U mesh mentioned in I st method which I have solved by replacing n with 0 to 6 as first day being one and one to understand easily. Thanks U mesh for reminding me the second method of applying log.
shasthranaam Ganitham moordhanisthitham

• Shouldn't it be (n-1) instead of n in the formula. With simply n and for n=7, the total is coming to 2315 (128+2187) instead of 793. Just check again. Am I missing something?
Patience and perseverance pays

• Yes you are correct Dhruv And I have edited my response accordingly. But while answering I have done plainly as a child
shasthranaam Ganitham moordhanisthitham

• @Rao&Partha

Nowadays it is not that tough if we put the input from second day onwards in an Excel by mere copy paste the formula and its total by swipe below we may get any number easily.

shasthranaam Ganitham moordhanisthitham

• Sarojah,
I agree with you. If we use computers and programmes to solve such questions, it will be easy only. But we will enjoy such puzzles by solving them traditionally.
What Dhruv said is correct. It should be n-1 only.

drrao
always confident

• What Dhruv Sir has stated is 200% correct. In actuality, I calculated the equation mentally and got the correct answer. But while writing the value of n, I wrongly wrote it 7 instead of 6. But, Sarojah Madam definitely gets the virtual gift as she was the first member to answer it correctly.
(a) Those who have forgotten Noakhali, how can they protest Sandeshkhali?
(b) Have no fear of perfection - you'll never reach it. ---------- Salvador Dali

• Sarojah is first to give the correct answer and congratulation to her for the virtual award from ISC gallery.
Thoughts exchanged is knowledge gained.

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