BrainDen.com - Brain Teasers

# bonanova

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2. ## Replacing Tiles

6 x 4 should be 2 81 x 63 should be 135 6x4 ruins at least the two corner tiles. Nothing else?
3. ## Airline tickets

Thanks, chocchief, your post has it right. We can't seem to distinguish Lois from Jean in our solutions.

6. ## The sums of fourth power numbers

dm92 asks for info on Newton method. Several links out there, this one is OK. http://m.youtube.com/watch?v=ER5B_YBFMJo&feature=related Successive approximations. You solve f(x)=0. You give an initial guess x0. Then x1 = x0 - f(x0)/f'(x0). Repeat. In several dimensions, like this problem with real numbers a x and y, the functions are f1 = 6-sum abc f2 = 8-sum2 abc f3 = 5-sum3 abc Calculate a 3x3 matrix M of partial derivatives of f123 wrt axy Guess axy, and repeat axy = axy - M-1 x f123 You can use delta's to approximate the derivatives if f is messy.

9. ## The sums of fourth power numbers

Interesting result!
10. ## A man travels between five cities

The old traveling salesman problem. Tractable for five cities, but unimaginably complex with just a few more cities.

12. ## Airline tickets

This is not an easy puzzle.

16. ## Balls in the corner

I'm thinking one of the walls must be the floor.

SP and Xavier both have it. SP by a nose. Nice solve both. Xavier, welcome to active duty! BobbyGo made an assumption which only holds when the halls are of equal widths, But provided a maximum ladder thickness as well.

Two hallways, of widths 4 and 6 feet, meet at a corner. You and a friend are borrowing a 14-foot ladder and need to get it past the corner. If the ends of the ladder are kept at the same height, is it possible to carry the ladder from one hallway to the next? What is the longest ladder that can pass?
19. ## Three Big Wheels

How much of the area of a 3 4 5 right triangle can be covered by three non overlapping circles completely contained by the triangle?
20. ## Division of a Will

Just a comment that Busindo's solution is attractive in that the inheritors have a hand in determining their benefit.