The first rule of a place like brilliant or any textbook for that matter is that the problem given must have a solution. Knowing that, you can look for one.

]]>You said some part of the above solution was tough. Which one? I will explain it further.

]]>There is a whole thread on it.

]]>Computer methods are basically the same as shown but thousands of times faster and with no errors.

]]>That is easy to do in your head.

I could do that, but the rest were tough.

What is the computer method for this?

]]>So you have a new equation:

30 a + 70 c + 105 d = 425

divide by 5:

6a + 14c + 21d = 85

Again 6 and 21 are divisible by 3 and 14 isn't so pick out the14:

85 - 14 c = {71,57,43,29,15,1} for c = 1,2,3,4,5,6

So only c =2 and c = 5 yields a number that is divisible by 3. Picking the 5 for c we

6a + 21 d = 15 which is impossible so c = 2 and you are left with this diophantine equation:

6 a + 21 d = 57

That is easy to do in your head. If you can not then continue as I have done,

a = 6, d = 1, c = 2, b =4

]]>next,please;

]]>That is the result of 593 - 42b for b = 1 to 15. It is only arithmetic and can be done in your head in less than 5 minutes. You see that only

593 - 4 x 42 = 425

593 - 9 x 42 = 215

Those are the only 2 divisible by 5.

Now you cannot partition 215 using { 30, 70, 105 } so 4 must be the answer.

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