Slanted rows?

Probability Level 2

This triangular lattice consists of four horizontal rows of 1,3,5, and 7 triangles respectively:

If each triangle were filled with an integer, is it possible that the sum of the integers for any horizontal row is odd, however the sum of each of the remaining eight "slanted rows" is even?

No Yes

Geoff Pilling by Geoff Pilling , 53, USA

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2 solutions

Chris Lewis
May 8, 2019

Using orange to represent odd integers and blue to represent evens, we can solve a smaller problem first...

...then put four of these together to get:

Or put two of these with two all even triangles:

1 Helpful 0 Interesting 1 Brilliant 0 Confused
Geoff Pilling
May 7, 2019

Yes. One example is if you fill the horizontal rows with:

  • 1
  • 010
  • 00001
  • 0000010
0 Helpful 1 Interesting 0 Brilliant 0 Confused

I arranged E(vens) and O(dds) in general and came up with this example for filling the horizontal rows:

O \space \space \space \space \space \space \space \space \space \space \space O

O O O \space \space \space \space \space \space \space \space O O O

O E O E O \space \space \space \space O E O E O

E E O O O E E E E O O O E E

Brian Charlesworth - 2 years, 1 month ago

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