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1998 (Posted on 2013-12-05) Difficulty: 3 of 5
(1)Is there an integer N such that 1998*N = 22222.......22222 (only the digit 2 in the expression of this number)? If so, how many digits are in N?

(2)A pocket calculator is broken. It is only possible to use the function keys: + , - , =, 1/x(inverse function). All number keys and the memory funtion work. How can we calculate the product 37 * 54? (The result is obviously 1998.)

(3)Is it true that 11111^99999 + 99999^88888 is divisible by 1998? Same question with 111111^999999 + 999999^888888 ?

No Solution Yet Submitted by Danish Ahmed Khan    
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Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some ways to do 2Jer2013-12-05 15:55:41
re: Just the first -- UBASIC code agreesCharlie2013-12-05 15:50:09
Some Thoughtspart 3 using UBASICCharlie2013-12-05 15:46:56
Some Thoughtspart 2?Charlie2013-12-05 15:42:00
Some ThoughtsJust the firstJer2013-12-05 15:15:47
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