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Puzzle 57
Can you complete the grid without forming a 3-In-A-Row of the same colour?
Each row and column has an equal number of Blue and White squares.
This puzzle has been added to the collection of logic puzzles that change daily on BrainBashers. Click the link at the top of the page to see today's puzzles.
Hint
Remember that you can't have three White or Blue squares together in a row or column.
Answer
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Puzzle 58
Disastrous Dave was washing windows on a multi-storey office building when he took a fall off a fifty-foot ladder, directly onto the concrete pavement below.
Hint
The largest possible difference is when 1 is next to 8, a difference of 7. Since we have 7 differences to find, and the largest possible difference is 7, all of the possible differences must exist. Start by looking where can the 8 go.
Answer
Reasoning
The largest possible difference is when 1 is next to 8, a difference of 7. Since we have 7 differences to find, and the largest possible difference is 7, all of the possible differences must exist: 1, 2, 3, 4, 5, 6, 7, and let's call these D1, …, D7.
D7 can only happen when: 1 is next to 8 = D7
D6 can happen when:
1 is next to 7, but these are given numbers that are not next to each other. 2 is next to 8 = D6
Where can we place the 8? If we put 8 above 1, we cannot also satisfy D6 (2 is next to 8).
Therefore, we have two possibilities:
(a) 8 to the left of 1
(b) 8 to the right of 1 (a) 8 to the left of 1
By D6, 2 would be below 8, and this would give us D1, D6, D7. What can we place to the right of 1?
Not 3, because the difference between 1 and 3, and the difference between 3 and 5, are both D2.
Not 4, because the difference between 4 and 5 is D1, which we would already have.
Not 6, because the difference between 5 and 6 is D1, which we would already have.
There are no possible numbers we can place to the right of 1, so 8 can't go to the left of 1. (b) 8 to the right of 1
By D6, 2 would be above 8, and this would give us D3, D6, D7.
4 can't go next to 1, otherwise we'd create another D3. Therefore, 4 goes in the bottom left corner.
We are now left with 3 and 6.
If 6 went above 4, and 3 above 1, these would both be D2.
It is now four years since I first asked for support, and I would like to sincerely thank everyone who has helped me. BrainBashers doesn't show adverts, and I continue to depend on the ongoing support from everyone who enjoys the site.
