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Prove that

(2 + √2)(3 - 2√2)n + (2 - √2)(3 + 2√2)n

is an integer for every positive integer n.
(No Solution Yet, 0 Comments) Submitted on 2024-07-26 by Danish Ahmed Khan    

 +-----+------+-----+----+
 | NN  | OUSE | AI  | BL |
 +-----+------+-----+----+
 | MI  |  DO  | EON | SI |
 +-----+------+-----+----+
 | LIC |  MA  | NR  | EP |
 +-----+------+-----+----+
 | NG  |  UB  | NI  | YO |
 +-----+------+-----+----+
 | CA  | CILY | DU  | SE |
 +-----+------+-----+----+
(i) Top Beach Vacation Destination	D•••••••• R••••••• (9, 8)
(ii) European Region S••••• (6)
(iii) Item of Clothing b••••• (6)
(iv) Downstairs d•••••• (7)
(v) Hamburger Ingredient m••••••••• (10)
• Combine groups of letters to create words.
• Each clue has one word associated with it.
• "N letters" shows how many letters each answer has.
(No Solution Yet, 1 Comments) Submitted on 2024-07-26 by K Sengupta    

In a game show, there is a certain game in which there are four hidden digits. There are no numbers greater than six among them, and no zeros.

You roll a die and then guess if the first digit is higher or lower than what you rolled. (If the die you rolled is equal to the first digit, you win no matter what you said.) You then roll and guess for each of the other three digits.

If you use the best strategy each time when saying "higher" or "lower", what is the chance you will get all four right and win? (Keep in mind you have no idea what the 4 digit number is.)

(No Solution Yet, 1 Comments) Submitted on 2024-07-25 by K Sengupta    

Suppose you have two candles of the same height but of different widths. One takes four hours to burn all the way while the other takes 7 hours.

Assuming both the candles burn down at steady rates, how long will it taken before one candle is twice as tall as the other?

(No Solution Yet, 1 Comments) Submitted on 2024-07-25 by K Sengupta    

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