Today's Puzzle

Kari said:

tom982 said:

And the last four :)


7=2*0+1+3!
8=2^(0*1+3)
9=(2+0+1)*3
10=(2*0+1+3)!

Tom, the last one is wrong: (2*0+1+3)! = 4! = 24

7, 8 and 9 are correct.

Oh crap In a moment of madness, I thought 4! = 4+3+2+1.


10=20/(-1+3)

Correct!

You guys are using notations beyond me.

Britton, the ! in math is a factorial.

For example:
4! = fact(4) = 1*2*3*4=24
7! = fact(7) = 1*2*3*4*5*6*7=5040

Funny enough, don't ask me why, the 0! = fact(0) = 1. Trying to find an explanation I just Googled "Math 0!" and got this page: Math Forum: Ask Dr. Math FAQ: 0! = 1

Thanks Kari! In Colin's solution what does the 1) mean?

Britton30 said:

Thanks Kari! In Colin's solution what does the 1) mean?

You mean this:

Golden said:

5 = ((2 + 0) x 1) + 3

You count first the formula within the first (blue) parenthesis 2 + 0 which gives 2, then using that sum you solve the formula within next (green) parenthesis using the sum from first parenthesis as a factor, 2 * 1 = 2.

Without (double) parenthesis it would be 2 + 0 x 1 + 3 = 5, so although the parenthesis are correct in this formula from Colin, they are this time unnecessary.

An example where using parenthesis would give a different outcome:
2 * 0 + 1 + 3 = 4
2 * (0 + 1) + 3 = 5

Ahh, I missed the first double parenthesis.

No special skills needed, just addition:

A three by three table:

And 9 prime numbers: 7, 37, 43, 67, 73, 79, 103, 109, 139

Place the given prime numbers so that each horizontal, vertical and diagonal line gives the exactly same sum. For instance if you think that the first row should be 73 + 103 + 7 = 183, then the two other horizontal lines, all three vertical lines and both diagonal lines should also give 183.

If this is too difficult, I will tell what the sum of all 8 lines should be :).

First hint: Each line gives a sum of 219.

solution:

Code:

 103    7   109
  79   73    67
  37  139    43

How did I arrive at the solution?
I don't know if this works in every case, but I used some logic as follows.

• given: 3,37,43,67,73,79,103,109,139
• the sum of the numbers is 657
• for the sum of each row or column to be equal, the sum has to be 657/3=219
• because there are 9 squares, I decided to divide the total by 9 and see what comes up: 657/9=73
• looking at the sequence, I found 73 to be the median --> why not try that in the center square?
• so 219-73=146 --> is there a pattern?
• the sums of the outer pair, second from outer pair, etc. all are 146
• this provides the following pairs: 7,139; 37,109; 43,103; 67,79
• because a center out perspective is working so far, let's examine using the two center pairs above (37,109; 43,103) for the diagonals
• placing the pairs in diagonal opposite corners provides the same sums as calculatd earlier for the rows and columns
• remaining squares are just a matter of simple math to provide a column or row sum of 219
• magically, all of these solutions used one of the remaining numbers given for the puzzle

I was posting my solution while you were providing the hint. I did not peak.