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 1998 (Posted on 2013-12-05)
(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 No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: Just the first -- UBASIC code agrees | Comment 4 of 5 |
(In reply to Just the first by Jer)

LIST
10   N=2
20   while N<22222222222222222222222222222222222222222222
25      if N @ 1998=0 then
30      :print N,N//1998,len(cutspc(str(N//1998)))
40      N=N*10+2
50   wend
OK
run
222222222222222222222222222     111222333444555666777889        24
OK

 Posted by Charlie on 2013-12-05 15:50:09

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