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Six Puzzles

Friday, February 25th, 2011 08:25 / 2 Comments

Assume that the English letters are digits (from 0 to 9 ) and they satisfy the given relations, then you have to solve each equation for these letters.

For Example:
ABCDE \times ABCDE = FDBABCDE can have a solution:
09376 \times 09376 = 87909376

Similarly, Try these:

1. ABCDEEABCD \times FEC = AAAAAAAAAAAA

2. (A+B+C+D+E) \times (A+B+C+D+E) \times (A+B+C+D+E) = ABCDE

3. 6 \times ABCDEF =DEFABC

4. ABCDEABCDEABCDE = C \times CCCCCGGGGH \times ABCDE

5. ABCDEABCDE = FF \times GHGF \times 86485

Solution:

1. 8547008547 \times 104 =888888888888
2. (1+9+6+8+3) \times (1+9+6+8+3) \times (1+9+6+8+3) =19683
3. 6 \times 14857 857142
4. 283512835128351 =3 \times 3333366667 \times 28351
5. 8648586485 =11 \times 9091 \times 86485

Puzzle Idea: Mr. Sawinder Singh, Gurdaspur, Punjab (INDIA)
Note:
There may be many other solutions for these puzzles too.

ramanujan

Solving Ramanujan’s Puzzling Problem

Thursday, February 3rd, 2011 14:07 / 11 Comments

Consider a sequence of functions as follows:-

f_1 (x) = \sqrt {1+\sqrt {x} }
f_2 (x) = \sqrt{1+ \sqrt {1+2\sqrt {x} } }

f_3 (x) = \sqrt {1+ \sqrt {1+2 \sqrt {1+3 \sqrt {x} } } }

……and so on to

f_n (x) = \sqrt {1+\sqrt{1+2 \sqrt {1+3 \sqrt {\ldots \sqrt {1+n \sqrt {x} } } } } }

Evaluate this function as n tends to infinity.

Or logically:

Find

\displaystyle{\lim_{n \to \infty}} f_n (x) .

(more…)

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