Someone please help me?

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2 Answers
Apr 15, 2018

337

Explanation:

You have been given the four numbers 12, 7, 4 and 1 and the only other thing you can do with this is add, subtract, multiply or divide.

I used 12, 7 and 4 to multiply them together:

1274=336

You could multiply by 1 as well, but this will just give you 336.
You do not want to subtract, otherwise, this will reduce the value, and division will give you 336, so the addition is all that's left.

336+1=337

So to show this, use brackets to separate the functions:
(1274)+1=337

Further explanation:

Multiplication is thought as repeated addition (copies of the same value) wheras division is used to separate the value into equal divisions. Subtraction reduces the number and addition increases. So the best method to get the largest possible value is by multiplication. If powers could be used, then this would make the end value even larger.

Apr 15, 2018

(4+1)127=420

Explanation:

The numbers p and q get the highest result by multiplication, if they are (p,q)2. Therefore, for 12,4,7 the highest result is
1247=336
But what do we do with the one? If we multiply, the result will be the same, just like when we divide. Subtraction will make the result samller, therefore we add 1. Lets go through the possibilities:

Adding to the existing result:
336+1=337
Adding to the 12:
(12+1)47=364
Adding to the 4:
12(4+1)7=420
Adding to the 7:
124(7+1)=384
The smaller the product is we are adding 1 to, the higher the result is going to be. Here is why:

Let 1<a<b<c:

ab(c+1)=abc+ab
a(b+1)c=abc+ac
(a+1)bc=abc+bc
ab<ac<bc