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Project Euler Problem 29 Solution

Problem Description

Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:

22=4, 23=8, 24=16, 25=32
32=9, 33=27, 34=81, 35=243
42=16, 43=64, 44=256, 45=1024
52=25, 53=125, 54=625, 55=3125

If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:

4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?

Analysis

Build a set of distinct ab terms using Python’s set data type and print the set’s length.

Solution

Runs < 1 second in Python.

```h=set() for a in range(2,101): for b in range(2,101): h.add(a**b)   print "Answer to PE29 = ",len(h);```

• Python supports large integers inherently.
• The answer for ab for 2 ≤ a ≤ 200 and 2 ≤ b ≤ 200 is 37,774
and for 2 ≤ a ≤ 1000 and 2 ≤ b ≤ 1000 is 977,358.
• Mathematica: Length@Union@Flatten@Table[a^b,{a,2,100},{b,2,100}]

Discussion

2 Responses to “Project Euler Problem 29 Solution”

1. You teach me a lot,
Many thanks to you.

Posted by ye wang | August 25, 2012, 6:55 AM
2. You’re welcome Ye, it is my pleasure.

Posted by Mike | August 25, 2012, 11:24 AM