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Eight Calculations (Posted on 2013-08-29) Difficulty: 3 of 5
 \   ↓       ↓       ↓  /
   +---+---+---+---+---+  
  →| 4 | x |   | + |   | =?
   +---+---+---+---+---+  
   | x | x | + | x | x |
   +---+---+---+---+---+               
  →|   | - |   | x | 3 | =?
   +---+---+---+---+---+  
   | + | + | x | + | - |
   +---+---+---+---+---+    
  →|   | x | 5 | x |   | =?
   +---+---+---+---+---+ 
=?  =        =       =   =?
    ?        ?       ? 
Place the integers from 1 to 9 inclusive into the gaps in the above diagram. (The numbers 3, 4 and 5 have already been placed.)

When all the numbers are correctly placed in appropriate positions, there should be eight calculations the solutions to which should contain the same digits as the integers from 0 to 12 inclusively. (For example: 30, 12 and 45 has the same digits as integers from 0 to 5 inclusively, albeit these constitute part of the actual solution.)
  1. The eight solutions should contain a two digit positive integer between 10 and 90 inclusively in place of each question mark.
  2. There are three vertical, three horizontal and two diagonal calculations, the start of which is indicated by the appropriate arrow.
  3. The symbols used are: addition (+), subtraction (-) and multiplication (x).
Order of operations: Multiplication(x), then addition(+) and then subtraction(-).

No Solution Yet Submitted by K Sengupta    
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Solution Solution, assuming error in text Comment 1 of 1
The second horizontal calculation has a maximum value of 9-1*3=6, which does not fall in the 10 to 90 range stipulated.  Then I assume the 'order of operations' statement is in error and that the calculations are to be done in a strictly left-to-right manner.

Then I find one solution where the calculated values use the digit set {0011111223456789}:
    4 * 7 + 9 = 37
* * + * *
6 - 1 * 3 = 15
+ + * + -
2 * 5 * 8 = 80
= = = = =
11 26 40 19 12

  Posted by Brian Smith on 2017-06-24 09:07:13
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