P035 : Tangents to a Circle

P034 : Tangents to a Hyperbola

P033 : Integration 4

P032 : Integration 3

P031 : Hero's Formula

P030 : Integration 2

P029 : Summation 5

P028 : Arithmetic Progression

P027 : Equation of a Circle

P026 : Binomial Theorem

P025 : Difference Equation

P024 : Summation 4

P023 : Summation 3

P022 : Cramer's Rule

P021 : Linear Regression

P020 : Chinese Remainder Theorem

P019 : Tower of Hanoi

The Tower of Hanoi can be played using paper and pen only. The following is a solution of the game with 6 disks represented by the numbers 1,2,3,4,5,6 where disk i is smaller than disk i+1, i=1,2,3,4,5. The poles are represented by the letters A, B, C.
Explanation : In step (01), disk 1 is transferred from pole A to pole B.
(00) (123456,,)
(01) (23456,1,) (AB)
(02) (3456,1,2) (AC)
(03) (3456,,12) (BC)
(04) (456,3,12) (AB)
(05) (1456,3,2) (CA)
(06) (1456,23,) (CB)
(07) (456,123,) (AB)
(08) (56,123,4) (AC)
(09) (56,23,14) (BC)
(10) (256,3,14) (BA)
(11) (1256,3,4) (CA)
(12) (1256,,34) (BC)
(13) (256,1,34) (AB)
(14) (56,1,234) (AC)
(15) (56,,1234) (BC)
(16) (6,5,1234) (AB)
(17) (16,5,234) (CA)
(18) (16,25,34) (CB)
(19) (6,125,34) (AB)
(20) (36,125,4) (CA)
(21) (36,25,14) (BC)
(22) (236,5,14) (BA)
(23) (1236,5,4) (CA)
(24) (1236,45,) (CB)
(25) (236,145,) (AB)
(26) (36,145,2) (AC)
(27) (36,45,12) (BC)
(28) (6,345,12) (AB)
(29) (16,345,2) (CA)
(30) (16,2345,) (CB)
(31) (6,12345,) (AB)
(32) (,12345,6) (AC)
(33) (,2345,16) (BC)
(34) (2,345,16) (BA)
(35) (12,345,6) (CA)
(36) (12,45,36) (BC)
(37) (2,145,36) (AB)
(38) (,145,236) (AC)
(39) (,45,1236) (BC)
(40) (4,5,1236) (BA)
(41) (14,5,236) (CA)
(42) (14,25,36) (CB)
(43) (4,125,36) (AB)
(44) (34,125,6) (CA)
(45) (34,25,16) (BC)
(46) (234,5,16) (BA)
(47) (1234,5,6) (CA)
(48) (1234,,56) (BC)
(49) (234,1,56) (AB)
(50) (34,1,256) (AC)
(51) (34,,1256) (BC)
(52) (4,3,1256) (AB)
(53) (14,3,256) (CA)
(54) (14,23,56) (CB)
(55) (4,123,56) (AB)
(56) (,123,456) (AC)
(57) (,23,1456) (BC)
(58) (2,3,1456) (BA)
(59) (12,3,456) (CA)
(60) (12,,3456) (BC)
(61) (2,1,3456) (AB)
(62) (,1,23456) (AC)
(63) (,,123456) (BC)
The number of steps required to solve the game of Tower of Hanoi of n disks is 2^n-1 where n is the number of disks.
In the example above, note that the number of steps taken = 63 = 2^6-1.
Strategy : When transferring the disks, make sure that the numbers representing the adjacent disks differ by an odd number.

P018 : Finding integer solutions of ax+by=c where gcd(a,b)|c

P017 : tan (7.5 degrees)

P016 : Integrate e^ax sin bx

P015 : sin (18 degrees)