## Problem:

Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 134468.

Similarly if no digit is exceeded by the digit to its right it is called a decreasing number; for example, 66420.

We shall call a positive integer that is neither increasing nor decreasing a "bouncy" number; for example, 155349.

As n increases, the proportion of bouncy numbers below n increases such that there are only 12951 numbers below one-million that are not bouncy and only 277032 non-bouncy numbers below 1010.

How many numbers below a googol (10100) are not bouncy?

5537376230

## Code:The solution may include methods that will be found here: Library.java .

public interface EulerSolution{public String run();}
/*  * Solution to Project Euler problem 13 * By Nayuki Minase *  * http://nayuki.eigenstate.org/page/project-euler-solutions * https://github.com/nayuki/Project-Euler-solutions */import java.math.BigInteger;public final class p013 implements EulerSolution {		public static void main(String[] args) {		System.out.println(new p013().run());	}			public String run() {		BigInteger sum = BigInteger.ZERO;		for (String num : NUMBERS)			sum = sum.add(new BigInteger(num));		return sum.toString().substring(0, 10);	}			private static String[] NUMBERS = {		"37107287533902102798797998220837590246510135740250",		"46376937677490009712648124896970078050417018260538",		"74324986199524741059474233309513058123726617309629",		"91942213363574161572522430563301811072406154908250",		"23067588207539346171171980310421047513778063246676",		"89261670696623633820136378418383684178734361726757",		"28112879812849979408065481931592621691275889832738",		"44274228917432520321923589422876796487670272189318",		"47451445736001306439091167216856844588711603153276",		"70386486105843025439939619828917593665686757934951",		"62176457141856560629502157223196586755079324193331",		"64906352462741904929101432445813822663347944758178",		"92575867718337217661963751590579239728245598838407",		"58203565325359399008402633568948830189458628227828",		"80181199384826282014278194139940567587151170094390",		"35398664372827112653829987240784473053190104293586",		"86515506006295864861532075273371959191420517255829",		"71693888707715466499115593487603532921714970056938",		"54370070576826684624621495650076471787294438377604",		"53282654108756828443191190634694037855217779295145",		"36123272525000296071075082563815656710885258350721",		"45876576172410976447339110607218265236877223636045",		"17423706905851860660448207621209813287860733969412",		"81142660418086830619328460811191061556940512689692",		"51934325451728388641918047049293215058642563049483",		"62467221648435076201727918039944693004732956340691",		"15732444386908125794514089057706229429197107928209",		"55037687525678773091862540744969844508330393682126",		"18336384825330154686196124348767681297534375946515",		"80386287592878490201521685554828717201219257766954",		"78182833757993103614740356856449095527097864797581",		"16726320100436897842553539920931837441497806860984",		"48403098129077791799088218795327364475675590848030",		"87086987551392711854517078544161852424320693150332",		"59959406895756536782107074926966537676326235447210",		"69793950679652694742597709739166693763042633987085",		"41052684708299085211399427365734116182760315001271",		"65378607361501080857009149939512557028198746004375",		"35829035317434717326932123578154982629742552737307",		"94953759765105305946966067683156574377167401875275",		"88902802571733229619176668713819931811048770190271",		"25267680276078003013678680992525463401061632866526",		"36270218540497705585629946580636237993140746255962",		"24074486908231174977792365466257246923322810917141",		"91430288197103288597806669760892938638285025333403",		"34413065578016127815921815005561868836468420090470",		"23053081172816430487623791969842487255036638784583",		"11487696932154902810424020138335124462181441773470",		"63783299490636259666498587618221225225512486764533",		"67720186971698544312419572409913959008952310058822",		"95548255300263520781532296796249481641953868218774",		"76085327132285723110424803456124867697064507995236",		"37774242535411291684276865538926205024910326572967",		"23701913275725675285653248258265463092207058596522",		"29798860272258331913126375147341994889534765745501",		"18495701454879288984856827726077713721403798879715",		"38298203783031473527721580348144513491373226651381",		"34829543829199918180278916522431027392251122869539",		"40957953066405232632538044100059654939159879593635",		"29746152185502371307642255121183693803580388584903",		"41698116222072977186158236678424689157993532961922",		"62467957194401269043877107275048102390895523597457",		"23189706772547915061505504953922979530901129967519",		"86188088225875314529584099251203829009407770775672",		"11306739708304724483816533873502340845647058077308",		"82959174767140363198008187129011875491310547126581",		"97623331044818386269515456334926366572897563400500",		"42846280183517070527831839425882145521227251250327",		"55121603546981200581762165212827652751691296897789",		"32238195734329339946437501907836945765883352399886",		"75506164965184775180738168837861091527357929701337",		"62177842752192623401942399639168044983993173312731",		"32924185707147349566916674687634660915035914677504",		"99518671430235219628894890102423325116913619626622",		"73267460800591547471830798392868535206946944540724",		"76841822524674417161514036427982273348055556214818",		"97142617910342598647204516893989422179826088076852",		"87783646182799346313767754307809363333018982642090",		"10848802521674670883215120185883543223812876952786",		"71329612474782464538636993009049310363619763878039",		"62184073572399794223406235393808339651327408011116",		"66627891981488087797941876876144230030984490851411",		"60661826293682836764744779239180335110989069790714",		"85786944089552990653640447425576083659976645795096",		"66024396409905389607120198219976047599490197230297",		"64913982680032973156037120041377903785566085089252",		"16730939319872750275468906903707539413042652315011",		"94809377245048795150954100921645863754710598436791",		"78639167021187492431995700641917969777599028300699",		"15368713711936614952811305876380278410754449733078",		"40789923115535562561142322423255033685442488917353",		"44889911501440648020369068063960672322193204149535",		"41503128880339536053299340368006977710650566631954",		"81234880673210146739058568557934581403627822703280",		"82616570773948327592232845941706525094512325230608",		"22918802058777319719839450180888072429661980811197",		"77158542502016545090413245809786882778948721859617",		"72107838435069186155435662884062257473692284509516",		"20849603980134001723930671666823555245252804609722",		"53503534226472524250874054075591789781264330331690",	};	}