Adding Multiples 2

Directions: Using the digits 0 to 9, at most one time each, fill in the boxes to make a true statement with the greatest possible total.

Hint

HINT GOES HERE

Answer

The greatest total we’ve found so far is 83 which comes from (9 x 7) + (5 x 4). Do you have a greater total? Let us know in the comments.

Source: Owen Kaplinsky and Robert Kaplinsky

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Directions: Using the digits 1 to 9 at most one time each, place a digit …

13 comments

  1. Traut Core Knowledge 4th Grade Ms. Petros’ class got 96. (9 x 8) + (4 x 6).

  2. Traut Core Knowledge 4th Grade Ms. Petros’ Class got 96. (9×8) + (6×4)

  3. You are using the 9 twice. Breaking the stated rules.

  4. I got 115 with ( 9 x 8 ) + ( 7 x 6 )

  5. You can’t have a 3 digit product.

  6. An exhaustive search yields the greatest answer is (9 x 7) + (5 x 4) = 83.
    Here is the code:
    import itertools
    max_answer = 0
    valid_answer_count = 0
    for trial in itertools.permutations(range(0,10),4):
    answer = trial[0]*trial[1]+trial[2]*trial[3]
    answer_ones = answer % 10
    answer_tens = answer // 10
    if (answer_ones in trial): continue
    if (answer_tens in trial): continue
    if (answer_ones == answer_tens): continue
    if (answer > 99): continue
    #print(trial,answer)
    valid_answer_count += 1
    if (answer > max_answer):
    max_answer = answer
    max_trials = trial
    print(“#Valid answers:”, valid_answer_count,”Max answer:”,max_answer,max_trials)

    and the result:
    #Valid answers: 1144 Max answer: 83 (4, 5, 7, 9)

    • And here are all the unique answers with a representative expression that results in the answer:
      12 = (9*0) + (4*3)
      14 = (9*0) + (7*2)
      16 = (9*0) + (8*2)
      18 = (9*2) + (7*0)
      20 = (8*1) + (4*3)
      21 = (9*0) + (7*3)
      24 = (9*1) + (5*3)
      25 = (7*3) + (4*1)
      26 = (7*3) + (5*1)
      27 = (9*3) + (8*0)
      28 = (9*0) + (7*4)
      29 = (8*3) + (5*1)
      30 = (7*4) + (2*1)
      32 = (9*0) + (8*4)
      36 = (9*4) + (8*0)
      37 = (8*4) + (5*1)
      38 = (9*4) + (2*1)
      39 = (8*4) + (7*1)
      41 = (9*3) + (7*2)
      42 = (9*0) + (7*6)
      43 = (8*1) + (7*5)
      45 = (7*6) + (3*1)
      46 = (8*5) + (3*2)
      47 = (9*5) + (2*1)
      48 = (9*5) + (3*1)
      50 = (9*4) + (7*2)
      51 = (9*3) + (6*4)
      52 = (8*6) + (4*1)
      54 = (9*6) + (8*0)
      56 = (9*0) + (8*7)
      57 = (9*6) + (3*1)
      58 = (9*6) + (4*1)
      59 = (8*7) + (3*1)
      60 = (9*4) + (8*3)
      61 = (9*5) + (8*2)
      62 = (9*3) + (7*5)
      63 = (9*7) + (8*0)
      65 = (9*7) + (2*1)
      67 = (9*3) + (8*5)
      68 = (9*7) + (5*1)
      70 = (9*6) + (8*2)
      72 = (9*8) + (6*0)
      74 = (9*8) + (2*1)
      75 = (9*8) + (3*1)
      76 = (9*8) + (4*1)
      81 = (9*7) + (6*3)
      82 = (9*6) + (7*4)
      83 = (9*7) + (5*4)

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