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By Arthur Wouk

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Multiply the number by 6. Add 8 to the product. Divide the sum by 2. Subtract 4 from the quotient. The resulting number is twice the original number. 16. Pick any counting number. Multiply the number by 8. Subtract 4 from the product. Divide the difference by 4. Add 1 to the quotient. The resulting number is twice the original number. 3. 3, 5, 9, 15, 23, 33, ? 4. 1, 8, 27, 64, 125, ? 5. 1, 4, 9, 16, 25, 36, 49, ? 6. 80, 70, 61, 53, 46, 40, ? 7. 3 5 7 9 11 13 , , , , , ,? 5 7 9 11 13 15 8. 1 2 3 4 5 6 , , , , , ,?

Allison wishes to walk along the streets from point A to point B. How many direct routes can Allison take? 1 City Map Solution A Understand the Problem We would not be able to answer the question if Allison retraced her path or traveled away from point B. Thus we assume that on a direct route, she always travels along a street in a direction that gets her closer to point B. 1 has many extraneous details. Thus we make a diagram that allows us to concentrate on the essential information. See the figure at the left.

The numbers . . , Ϫ3, Ϫ2, Ϫ1, 0, 1, 2, 3, . . are called integers. 9. 2, 7, Ϫ3, 2, Ϫ8, Ϫ3, Ϫ13, Ϫ8, Ϫ18, ? 10. 1, 5, 12, 22, 35, ? Experimental Data Galileo used inclines similar to the one shown below to meas- ure the distance balls of various weights would travel in equal time intervals. The conclusions that Galileo reached from these experiments were contrary to the prevailing Aristotelian theories on the subject, and he lost his post at the University of Pisa because of them. An experiment with an incline and three balls produced the following results.

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