Using only the numerical buttons of a calculator bring a total of 1000 by pressing the following: plus (+) sign: 24 times; 0 (zero): eight times; 1, 4, 5,6, 7, 8 and 9: four times; 2 and 3: six times.

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kk

  • Sep 12th, 2005
 

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ez3736

  • Jul 4th, 2007
 

First how to go about this type of question:

We have to press (+) sign for 24 times and we are not allowed to press (=) sign, so we have to make 1000 by adding 24 numbers.  Divide 1000 by 24, you get about 40 so all the 24 numbers must be two digit numbers.

Also, if we count all the digits in all the numbers it comes to 48 so that way also we are having 24 2 digit numbers.

8 zeros + 4 ones + 6 twos + 6 Threes + 4 fours + 4 fives + 4 sixs + 4 sevens +
4 eights + 4 nines = 48 digits / 24 = 2.  We are adding 24    two digit numbers.

Two ways you can find out.  One practicle which I did using XL. 
Another is theoretical.  Where you make equation like  Digit 2 can be at unit position or tenth position.  so sum of all such 24 number = 2 *( 10 * A + B) where x is A times at 10th position and B times at unit position and A+B = 6.  We have 20 such variable A and B and will have more than 21 equations so we can solve for each A and B.


Following are the numbers which I got after tring that in XL spread sheet for about 2 minutes.
01 + 01 + 11 + 02+02 +22+33+33+33+44+44+55+55+66+66+77+77+88+88+99+99+02+02+00+    (At this point calculator will show 1000)

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