Appendix C: Number Series Materials Number Series Instructions for Participants In the following you will be asked to answer a set of number series items. Each series consists of 8 numbers. Your task is to enter the number that comes next in the series. Each number in the series can be one- or two-digit positive integers. This applies to numbers in the series as well as the answer. Every series is based on a mathematical formula composed of one or more of three specific rules (multiple rules can be combined on one item): • Adding or subtracting a constant less than or equal to 20. • Adding the two previous terms of the series. • Calculating the checksum (the sum of the digits). For example, the checksum of 15 is 6. You can make yourself familiar with the principles of this test by looking at the following three example items. Example 1 (Subtracting a constant): 51, 46, 41, 36, 31, 26, 21, 16, ? Each term of the series is derived by subtracting 5 from the previous term. Hence the next term of the series is 16 – 5 = 11. Example 2 (Adding the two previous terms of the series): 2, 3, 5, 8, 13, 21, 34, 55, ? Each term after the second is obtained by adding the two previous terms. Thus the next term is 34 + 55 = 89. Example 3 (Add the checksum): 10, 11, 13, 17, 25, 32, 37, 47, ? Each term of this series is derived by adding the checksum of the previous term to the previous term. So for example, the checksum of the first term, 10, is 1, and 10 + 1 = 11. The checksum of 11 is 2, and 11 + 2 = 13. The checksum of 13 is 4, and 13 + 4 = 17. And so on. The checksum of 47 is 11 and 47 + 11 = 58. Thus the next term of the series is “58”. Please keep the following in mind when working on the items: • There is exactly one solution for each item. • Only the three specific rules listed above should be used to find the correct solution to a series. No credit is given for suggested solutions to the series based on different principles than the ones defined here. • An item can be based on one rule or on a combination of several rules. • Do not spend too much time on solving a specific item. The time for each item is limited to 1.5 minutes, and the total time allotted for all 35 questions is 30 minutes.