1. ## Problem solving...problem.

Here goes. I have to achieve the highest number possible equal to or less than 143. 143 is the ideal number, anything above that is of no use. The numbers I have to work with are 37, 73, 44, 44, 40, 52, 73, 34 and 39. The closest I've managed to get is 140 combining 44, 44 and 52. Can anyone find anything higher than 140 or another combination that makes 140? Thanks for your help.

2. What operations are you allowed to use? Are you only allowed to use addition? Or is subtraction, multiplication, or division also allowed?

3. Originally Posted by guildmage
What operations are you allowed to use? Are you only allowed to use addition? Or is subtraction, multiplication, or division also allowed?
Sorry, I forgot to mention. Only addition is allowed with this set of numbers.

4. I think that's as close you can get to 143. If subtraction is allowed, you can get to 143 exactly.

5. 44,44,52 is tops! None other.

6. Right, I've had a look at my figures and there are infact some that I can subtract. So now the question is: I need to get as close to 143 as I can without going over 143. The numbers that can be added to make this number are 37, 73, 44, 44, 40, 52, 73, 34 and 39. The numbers that can be subtracted to make this number are 42, 46, 28, 28, 59, 67, 60, 52, 114, 64 and 80. So you're allowed to go to 190(for example) and subtract 52 to reach 138. Thanks for your help.

7. What numbers have you tried to get as close to 143?

8. Well I've not tried using subtraction yet, so 140 using 44, 44 and 52 is still the best I can get.

9. Try it out for yourself first. It's possible to arrive at exactly 143 with those numbers and with subtraction.

10. There's many solutions.
Here's one using the -114: 34+37+40+73+73-114 = 143

Hint:
from the positives, get combos => 171; then see if combo can be REDUCED to 143;
example: with 171: 171-28 = 143