Find the rate problem

Problem 179 from http://mathproblems.info/group9.html

A drag racer accelerates at a uniform rate from its starting point. It travels the last one fourth of the distance from the starting point to the finish line in 3 seconds. How long did it take to travel the entire distance from starting point to finish line?

Accelerating race car

Accelerating race car

Find a buiried cable digging a trench

Problem nummber 110 from http://mathproblems.info/group6.html

There is a straight cable buried under a unit square field. You must dig one or more ditches to locate the buried cable. Where should you dig to guarantee finding the cable and to minimize digging? For example you could dig an X shape for total ditch length of 2*sqr(2) but there is a better answer.

Solution….

Finding a solution  - page one

Finding a solution - page one

continuing…

Finding a solution  - page two

Finding a solution - page two

continuing…

Finding a solution  - page three

Finding a solution - page three

12 ball weighing problem – find the fake

Problem 85 from http://mathproblems.info/group5.html

In front of you are 12 pearls, 11 being real and one fake. The real ones all weigh the same and the fake one differs in weight from the real ones (may weigh more or less). With a balance scale and three weighings how can you weed out the fake one and determine whether it is too heavy or too light?

Twelve pearls, one fake, and a scale

Twelve pearls, one fake, and a scale

River crossing problem with predators

Problem 79 from http://mathproblems.info/group4.html

One one side of a river are three humans, one big monkey, two small monkeys, and one boat. Each of the humans and the big monkey are strong enough to row the boat. The boat can fit one or two bodies (regardless of size). If at any time at either side of the river the monkeys outnumber the humans the monkeys will eat the humans. How do you get everyone on the other side of the river alive?

River crossing with predators

River crossing with predators

Descending 200 meters with a 150 meter rope

Saw this problem at http://gurmeetsingh.wordpress.com/puzzles/

A man is trapped atop a building 200m high. He has with him a rope 150m long. There is a hook at the top where he stands. Looking down, he notices that midway between him and the ground, at a height of 100m, there is a ledge with another hook. In his pocket lies a Swiss knife. Hmm… how might he be able to come down using the rope, the two hooks and the Swiss knife

Detect a palindrome

Devise an algorithm for detecting when a string is a palindrome. Ex: A man, a plan, a canal, Panama”.

(Another from: http://www1.cs.columbia.edu/~kns10/interview/)

Example palindromes I got from a quick web search. 

Don’t nod
Dogma: I am God
Never odd or even
Too bad – I hid a boot
Rats live on no evil star
No trace; not one carton
Was it Eliot’s toilet I saw?
Murder for a jar of red rum
May a moody baby doom a yam?
Go hang a salami; I’m a lasagna hog!
Satan, oscillate my metallic sonatas!
A Toyota! Race fast… safe car: a Toyota
Straw? No, too stupid a fad; I put soot on warts
Are we not drawn onward, we few, drawn onward to new era?
Doc Note: I dissent. A fast never prevents a fatness. I diet on cod
No, it never propagates if I set a gap or prevention
Anne, I vote more cars race Rome to Vienna
Sums are not set as a test on Erasmus
Kay, a red nude, peeped under a yak
Some men interpret nine memos
Campus Motto: Bottoms up, Mac
Go deliver a dare, vile dog!
Madam, in Eden I’m Adam
Oozy rat in a sanitary zoo
Ah, Satan sees Natasha
Lisa Bonet ate no basil
Do geese see God?
God saw I was dog
Dennis sinned