Open Middle®
Directions: Using the digits 1 to 9 at most one time each, place a digit in each box to make a true equation where x has the greatest possible value.
Hint
How do the constants’ values affect the variable’s value?
Which constant should have a greater value?
Which constant should have a lesser value?
Which constant should have a greater value?
Which constant should have a lesser value?
Answer
The greatest possible value of x is 85 when 12 + x = 97
Source: Robert Kaplinsky
The greatest value of x is 85 when 12+x =97
Nice Talayla!
85 + 12 = 97, x = 85
Of the 173 unique ways to place the digits 1 to 9 at most one time each in each box to make a true equation (119 if you don’t allow leading zeros), x is greatest in the equation 12 + x = 97 (x = 85) or 04 + x = 91 / 05 + x = 92 / 06 + x = 93 if you allow the digit 0 and smallest in the equations
35 + x = 47
36 + x = 48
37 + x = 49
38 + x = 50
46 + x = 58
47 + x = 59
48 + x = 60
57 + x = 69
58 + x = 70
63 + x = 75
73 + x = 85
74 + x = 86
78 + x = 90
83 + x = 95
84 + x = 96
85 + x = 97
or 39 + x = 41 if you allow zero
Correction: Without 0, there are 100 unique ways to place the digits 1 to 9 at most one time each in each box to make a true equation (times 4 because you could swap the addends, swap the tenths digits of the addends or swap the unit digits of the addends). With 0, there are 173 ways and with non-leading zeros there are 119 ways.