He needed to know that fact in order to solve the problem, and there must be only two different sets of age choices for the kids (one with twins one without twins) that produce equivalent A's and B's. It is not the fact that there are no twins, but the fact that the postman could NOT figure out the answer UNTIL he knew that there were no twins that is essential. Thus, there are two sets of three numbers x1, y1, & z1 and x2, y2, & z2 where x1 + y1 + z1 = x2 + y2 + z2 and x1 * y1 * z1 = x2 * y2 * z2. The most important piece of information in the puzzle is that there must be at least two sets of numbers that add together to give the same sum and multiply together to give the same product - or he would have been able to figure it out without the third parameter about the middle child (no twins). We know that the three ages are different because the 'middle' son has red hair, which implies that none of the children are twins. The basis for that solution is as follows: The postman's first statement tells us that x*y*z = A the postman's second statement tells us that x+y+z = B and the third statement tells us that x does not equal y does not equal z. The product of both are 40 and the sums are 14. With a little bit of work, you can discover that only one solution is possible: the kids must be 1, 5, and 8 because a solution with the same A and B involving twins (2, 2, and 10) is ruled out by the middle son with red hair. So the 70 cows finish off the field in 24 days. Now we set up the equation for 70 cows eating and the field growing for T days, until the grass is gone: In other words, in one day ten cows can eat as much as the field grows in three days.Now we substitute this back into either of the two starting equationsto find how much grass (N) was in the field at the start: Subtract the two equations and we get: 36Y - 120X = 0, or 36Y =120X or 3Y = 10X So we set up the equations for the amount of grass for the two cases, adding growing grass and subtracting eaten grass: At the end, the field has zero pounds of grass remaining. At the start the field already has N pounds of grass standing. The field grows Y pounds of grass per day. Let's say one cow can eat X pounds of grass per day. Now pay the man in the following way.ĭay 1: give him a single link (Pay = 1 link)ĭay 2: Exchange the single link with the double link (Pay = 2 links)ĭay 3: Give him a single link (Pay = 3 links)ĭay 4: Exchange the 3 links (single link and the 2 link chain)ĭay 5: Give him the single link (Pay = 5 links)ĭay 6: Exchange the single link for the double link (Pay = 6 links)ĭay 7: Give him the single link (Pay = 7 links) This will give you a single link (that has been cut), a chain of two links and a chain of four links. HOWEVER, one of our visitors has suggested that IF the worker agrees to not spend his pay until after the week is over AND to do an exchange most days, you can pay him each day by making only ONE cut in the chain. Then cutting each of those in the middle of the remaining two sections (of three links each) will divide the chain into individual links.

So first cutting the middle (fourth) link will yield a single link and two chains 3 links long. When you cut a link, you can remove the adjacent link from each side.

The chain can be divided with just three cuts. AND REMEMBER: You also have to count the time it takes to go back across the bridge with the flashlight!

Find a logical solution where all four people reach the other side safely in 17 minutes or less-but this solution cannot include having any of them go only halfway across, or go across in the dark, or throw the flashlight across, etc. There are only 17 minutes before the lava destroys the bridge. Two people crossing the bridge will travel at the speed of the slower person. Person #1 takes 1 minute, person #2 takes 2 minutes, person #3 takes 5 minutes, and person #4 takes 10 minutes. The people, suffering from different injuries, travel across the bridge at different speeds. Therefore, after 2 people cross safely, one has to go back to bring the flashlight back to the other side. Since it's dark, they must use a flashlight to cross. The bridge can only support 2 people at a time. There's a footbridge that spans the canyon. Four people, carrying only one flashlight, run for their lives. A volcano erupts in the dark of the night.

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