A Math Trick I Learned in the Street


The other day I was strolling in a part of the city where street vendors compete for the tourist dollar. I came across a young lady, felt marker in hand in front of an easel displaying a 6x6 array of numbers. It was a hot day, and it took an effort just to stand among the crowd at the same time understand what she was explaining. Curiosity won over me and here's what I found.

The 6x6 matrix was pre-filled with numbers from 1 to 36, incremented horizontally, i.e. the first row contains 1 to 6, the next 7 to 12, and so on until the last one which is 31 to 36.

She claimed that if we chose 6 numbers of our choice, she'd know the sum of the numbers, equal to 111!

I added the left diagonal, 1+8+15+22+29+36=111... it all made sense!
She asked me to choose a number, which I did, probably to her delight. I chose 1.

Then she explained that after my choice, she would circle the number I chose, and had to cross out, or exclude, all the numbers that are in the same column and row I chose, namely, 2,3,4,5,6,7,13,19,25,and 31.

Someone else chose 8. "Duh, you're playing her game!" I was thinking to myself as she merrily crossed out 7,9,10,11,12,2,14,20,26,32.

Fortunately a young boy chose 27, which was off-diagonal, followed by 18 suggested by his friend.

The truth came when 34 was circled and the number 23 was left on the board. I added the numbers circled, 1+8+27+18+34+23 ...sure enough, it was 111!

123456
789101112
131415161718
192021222324
252627282930
313233343536
I was late for my appointment, but was glad I learned a trick. I never found out what she was selling, or if she was selling anything at all!