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Simultaneous Operations - Pairs (Posted on 2012-03-03) Difficulty: 3 of 5

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possible solution | Comment 1 of 4
The following are the smallest pairs that fulfill both the given task and yields a positive value:
TASK I: (0,1)
0+1 =  1 : The Sum is Odd!
0-1 = -1 : The Difference is Odd!
0*1 =  0 : The Product is Even!
0/1 =  0 : The Quotient is an Integer!
If a leading zero is not permitted, then
TASK I: (2,1)
2+1 =  3 : The Sum is Odd!
2-1 =  1 : The Difference is Odd!
2*1 =  2 : The Product is Even!
2/1 =  2 : The Quotient is an Integer!

TASK II: (4,2)
4+2 =  6 : The Sum is Even!
4-2 =  2 : The Difference is Even!
4*2 =  8 : The Product is Even!
4/2 =  2 : The Quotient is an Integer!
If a leading zero is not permitted, then
TASK II: (2,1)
2+1 =  3 : The Sum is Odd!
2-1 =  1 : The Difference is Odd!
2*1 =  2 : The Product is Even!
2/1 =  2 : The Quotient is an Integer!

TASK III: (3,1)
3+1 =  4 : The Sum is Even!
3-1 =  2 : The Difference is Even!
3*1 =  3 : The Product is Odd!
3/1 =  3 : The Quotient is an Integer!

Assigning a different (positive) integer value to A,B,C,D,E,F,G and H where the pairs (AC, BD, GE and FH) yields a positive integer value and each pair is true for all four subtasks for at least one task -- the possible least values are:
(6,3 [Task I]),
(0,2 [Task II]),
(8,4 [Task II]), and
(5,1 [Task III]).
If a leading zero is not permitted, then the following may be the possible least values:
(6,2 [Task II]),
(8,4 [Task II]),
(5,1 [Task III]), and
(9,3 [Task III]).

  Posted by Dej Mar on 2012-03-03 13:05:02
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