Find the wrong number in the following series: 16 47 64 72 76 78 79

Concept: In a "find the wrong number" series problem, first test the differences between consecutive terms - forward and backward - for a consistent arithmetic, geometric, or doubling rule. The term whose actual difference deviates from that established rule is the wrongly printed number, and its corrected value follows directly from the rule.

Application: Reading the series 16, 47, 64, 72, 76, 78, 79 backward from the last term:

1. 79 to 78: difference = 1

2. 78 to 76: difference = 2

3. 76 to 72: difference = 4

4. 72 to 64: difference = 8

5. 64 to 47: difference = 17 - this breaks the doubling rule (1, 2, 4, 8, 16, 32); the required difference here is 16, so this term should be 64 minus 16 = 48, not 47

6. 48 to 16: difference = 32, which matches the doubling rule and confirms the series is consistent once 47 is replaced by 48

Cross-check: Working forward from 16 with the doubling gaps 32, 16, 8, 4, 2, 1 gives 16 + 32 = 48, 48 + 16 = 64, 64 + 8 = 72, 72 + 4 = 76, 76 + 2 = 78, 78 + 1 = 79 - exactly the rest of the given series. This confirms the rule and that only the printed term 47 fails to fit it.

Hence, 47 is the wrong number in the series (it should have been 48).