perplexus.info :: Numbers : Pi repeats

Pi repeats (Posted on 2012-02-29)

The Feynman point is a pattern in pi where the digit 9 repeats six times in a row. The 762nd to 767th digits are all 9. Here is pi to the Feynman point. Each row has 50 digits.

3.

14159265358979323846264338327950288419716939937510
58209749445923078164062862089986280348253421170679

82148086513282306647093844609550582231725359408128
48111745028410270193852110555964462294895493038196

44288109756659334461284756482337867831652712019091
45648566923460348610454326648213393607260249141273

72458700660631558817488152092096282925409171536436
78925903600113305305488204665213841469519415116094

33057270365759591953092186117381932611793105118548
07446237996274956735188575272489122793818301194912

98336733624406566430860213949463952247371907021798
60943702770539217176293176752384674818467669405132

00056812714526356082778577134275778960917363717872
14684409012249534301465495853710507922796892589235

42019956112129021960864034418159813629774771309960
51870721134999999...

1. Find three times where a digit repeats three times consecutively before the Feynman point.

2. The number 999 repeats twice consecutively in 999999. Find two 3-digit numbers that repeat twice consecutively before the Feynman point.

3. Find two 5-digit numbers that appear twice in different places before the Feynman point.

4. In one of the first 7 blocks of 100 digits, there is a 5-digit number ABCDE where ABCDE, ABCD, and BCDE all appear in different places in the same block. Which block of 100 digits is it, and what is ABCDE?

5. The number 999999 is of the form AABBAB, where A=B=9. Find a number of the form AABBAB before the Feynman point where A≠B.

6. Find a 6-digit number ABCDEF where ABCDEF and ABCDDEF both appear at different places before the Feynman point.

Submitted by Math Man

Rating: 5.0000 (1 votes)

Solution: (Hide)

1. 111, 555, 000
3.
14159265358979323846264338327950288419716939937510
58209749445923078164062862089986280348253421170679
82148086513282306647093844609550582231725359408128
48111745028410270193852110555964462294895493038196
44288109756659334461284756482337867831652712019091
45648566923460348610454326648213393607260249141273
72458700660631558817488152092096282925409171536436
78925903600113305305488204665213841469519415116094
33057270365759591953092186117381932611793105118548
07446237996274956735188575272489122793818301194912
98336733624406566430860213949463952247371907021798
60943702770539217176293176752384674818467669405132
00056812714526356082778577134275778960917363717872
14684409012249534301465495853710507922796892589235
42019956112129021960864034418159813629774771309960
51870721134999999...

2. 209, 305
3.
14159265358979323846264338327950288419716939937510
58209749445923078164062862089986280348253421170679
82148086513282306647093844609550582231725359408128
48111745028410270193852110555964462294895493038196
44288109756659334461284756482337867831652712019091
45648566923460348610454326648213393607260249141273
72458700660631558817488152092096282925409171536436
78925903600113305305488204665213841469519415116094
33057270365759591953092186117381932611793105118548
07446237996274956735188575272489122793818301194912
98336733624406566430860213949463952247371907021798
60943702770539217176293176752384674818467669405132
00056812714526356082778577134275778960917363717872
14684409012249534301465495853710507922796892589235
42019956112129021960864034418159813629774771309960
51870721134999999...

3. 23846, 60943
3.
14159265358979323846264338327950288419716939937510
58209749445923078164062862089986280348253421170679
82148086513282306647093844609550582231725359408128
48111745028410270193852110555964462294895493038196
44288109756659334461284756482337867831652712019091
45648566923460348610454326648213393607260249141273
72458700660631558817488152092096282925409171536436
78925903600113305305488204665213841469519415116094
33057270365759591953092186117381932611793105118548
07446237996274956735188575272489122793818301194912
98336733624406566430860213949463952247371907021798
60943702770539217176293176752384674818467669405132
00056812714526356082778577134275778960917363717872
14684409012249534301465495853710507922796892589235
42019956112129021960864034418159813629774771309960
51870721134999999...

4. Third block, 56482
44288109756659334461284756482337867831652712019091
45648566923460348610454326648213393607260249141273

5. 006606
3.
14159265358979323846264338327950288419716939937510
58209749445923078164062862089986280348253421170679
82148086513282306647093844609550582231725359408128
48111745028410270193852110555964462294895493038196
44288109756659334461284756482337867831652712019091
45648566923460348610454326648213393607260249141273
72458700660631558817488152092096282925409171536436
78925903600113305305488204665213841469519415116094
33057270365759591953092186117381932611793105118548
07446237996274956735188575272489122793818301194912
98336733624406566430860213949463952247371907021798
60943702770539217176293176752384674818467669405132
00056812714526356082778577134275778960917363717872
14684409012249534301465495853710507922796892589235
42019956112129021960864034418159813629774771309960
51870721134999999...

6. 502841
3.
14159265358979323846264338327950288419716939937510
58209749445923078164062862089986280348253421170679
82148086513282306647093844609550582231725359408128
48111745028410270193852110555964462294895493038196
44288109756659334461284756482337867831652712019091
45648566923460348610454326648213393607260249141273
72458700660631558817488152092096282925409171536436
78925903600113305305488204665213841469519415116094
33057270365759591953092186117381932611793105118548
07446237996274956735188575272489122793818301194912
98336733624406566430860213949463952247371907021798
60943702770539217176293176752384674818467669405132
00056812714526356082778577134275778960917363717872
14684409012249534301465495853710507922796892589235
42019956112129021960864034418159813629774771309960
51870721134999999...

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Happy Pi Day!	Math Man	2012-03-14 13:51:25
solutions	Dej Mar	2012-03-01 04:19:38
computer solution	Charlie	2012-02-29 15:35:48

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