Sometimes a good diagram can make all the difference. Consider this problem, which can make your head hurt just reading it. But with the right diagram,Duke the dog's head is 6 inches long, his tail is as long as his head plus half the length of his body, and his body is as long as the head and the tail combined. you're halfway to the solution.H = 6 +----+ T = H + B/2 | | ------------- +---------------+ +----- | | | | +---------------+ B = H + T Here's another example where a diagram changes something confusing into something straightforward:What day of the week was yesterday if 5 days before the day after tomorrow was Wednesday? +----------+----------+---------+-----+--------+---------+ |Day before|Day before|Yesterday|Today|Tomorrow|Day after| |day before|yesterday | | | |tomorrow | |yesterday | | | | | | +----------+----------+---------+-----+--------+---------+ ^ | |________ 5 days before the day after tomorrow Or consider this problem, and this diagram:Every day at noon a ship leaves San Francisco for Tokyo, and at the same instant a ship leaves Tokyo for San Francisco. Each trip lasts exactly eight days. How many Tokyo ships will each San Francisco ship meet? The right diagram can let you replace calculation with counting, or some other simple observation.Day |/ / / / / / / / | 0 X / / / / / / / * |\ / / / / / / / /| | X / / / / / / / | |/ \ / / / / / / / | 1 * X / / / / / / * | / \ / / / / / / /| | / X / / / / / / | |/ / \ / / / / / / | 2 * / X / / / / / * | / / \ / / / / / /| | / / X / / / / / | |/ / / \ / / / / / | 3 * / / X / / / / * | / / / \ / / / / /| | / / / X / / / / | |/ / / / \ / / / / | 4 * / / / X / / / * | / / / / \ / / / /| | / / / / X / / / | |/ / / / / \ / / / | 5 * / / / / X / / * | / / / / / \ / / /| | / / / / / X / / | |/ / / / / / \ / / | 6 * / / / / / X / * | / / / / / / \ / /| | / / / / / / X / | |/ / / / / / / \ / | 7 * / / / / / / X * | / / / / / / / \ /| | / / / / / / / X | |/ / / / / / / / \| 8 + / / / / / / / X | / / / / / / / /| SF Tokyo |