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

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

joe mama so fat

That doesn’t work. You used the number 9 twice

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

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

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

You can’t have a 3 digit product.

joe mama so fat

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)

This looks great! I’m assuming you used Python.

My 4th grade students offer this solution:

(9 X 8) + (6 X 4) = 72 + 24 = 96

Good try, but you used the 9 and the 6 both as factors and as digits in the product. You can’t repeat any of the digits used in the factors as digits of the product.