Lemma

Number Theory · Chapter 7 of 11

Digits

48 curated · 982 from open sources

← Diophantine equationsScales of notation →
AllEasyMediumDeep

Curated

48
#TitleDifficultySourceTags
23Adding 1 to 100A famous trickEasyLemmaPairingArithmetic series
592Digits of 2¹⁰DigitsEasyLemmaDigits
594Casting out ninesDigitsEasyLemmaDigits
595Units digit of 7⁷DigitsEasyLemmaDigits
596Last two digitsDigitsEasyLemmaDigits
597The eleven testDigitsEasyLemmaDigits
1096Base‑7 representationDigitsEasyHall & Knightbase conversionpositional notation
1097Base‑5 representationDigitsEasyHall & Knightbase conversionpositional notation
1098Binary representationDigitsEasyHall & Knightbase conversionbinary
1099Base‑3 representationDigitsEasyHall & Knightbase conversionpositional notation
1100Base‑9 representationDigitsEasyHall & Knightbase conversionpositional notation
1101Base‑4 to base‑5 conversionDigitsEasyHall & Knightbase conversionpositional notation
1108Convert from duodecimalDigitsEasyHall & Knightbase conversiondigits
1109Decimal to duodecimalDigitsEasyHall & Knightbase conversionfractional part
1110Ternary to nonaryDigitsEasyHall & Knightbase conversiongrouping digits
1111Septenary to vulgar fractionDigitsEasyHall & Knightbase conversionfraction reduction
1112Base for 182 as 222DigitsEasyHall & Knightbase conversionpositional notation
1510Value of 0.4 in base 7DigitsEasyHall & Knightbase conversionfractions
1511Value of 0.42 in base 7DigitsEasyHall & Knightbase conversionfractions
593How long is 2¹⁰⁰?DigitsMediumLemmaDigits
1081Sum in base‑5DigitsMediumHall & Knightadditionbase conversion
1082Sum in base‑9DigitsMediumHall & Knightadditionbase conversion
1083Subtraction in base‑8DigitsMediumHall & Knightsubtractionbase conversion
1084Base‑12 subtractionDigitsMediumHall & Knightsubtractionbase conversion
1085Division after subtraction in base‑6DigitsMediumHall & Knightsubtractiondivision+1
1086Multiplication in base‑7DigitsMediumHall & Knightmultiplicationbase conversion
1093Division in base‑sevenDigitsMediumHall & Knightbase conversiondivision
1095Square root in duodecimalDigitsMediumHall & Knightbase conversionsquare root
1102Duodenary to decimalDigitsMediumHall & Knightbase conversionpositional notation
1103Base‑12 to base‑11DigitsMediumHall & Knightbase conversionpositional notation
1104Senary to nonaryDigitsMediumHall & Knightbase conversionpositional notation
1105Base‑9 to base‑8DigitsMediumHall & Knightbase conversionpositional notation
1113Base for fraction 25/128 as 0.0302DigitsMediumHall & Knightbase conversionfraction representation
1114Radix where 554 is 24²DigitsMediumHall & Knightbase conversionquadratic equation
1115Base for 511197 as 1746335DigitsMediumHall & Knightbase conversionpolynomial evaluation
1117Base for geometric fractionsDigitsMediumHall & Knightradixgeometric progression
1118Changing base representationDigitsMediumHall & Knightbase conversionequality of values
1122Binary weights for a tonDigitsMediumHall & Knightbinary representationweights
1508GCM in base‑sixDigitsMediumHall & KnightGCDbase arithmetic
1787Digits in different scalesDigitsMediumHall & KnightBase representationDiophantine equations
1094Subtraction and square root in base‑eightDigitsDeepHall & Knightbase conversionsquare root
1106Nonary to quinaryDigitsDeepHall & Knightbase conversionpositional notation
1107Septenary to duodecimal powersDigitsDeepHall & Knightbase conversionpositional notation
1116Radix for arithmetic progressionDigitsDeepHall & Knightbase conversionarithmetic progression
1119Perfect square for large radicesDigitsDeepHall & Knightperfect squareradix representation
1120Square with invariant root digitsDigitsDeepHall & Knightperfect squareradix invariance
1121Universal perfect cubeDigitsDeepHall & Knightperfect cuberadix representation
1509LCM of several base‑six numbersDigitsDeepHall & KnightLCMbase arithmetic

From open sources

982

Complete problems only, with worked solutions first. Show everything

#TitleDifficultySource
10049Sam memorized six more digits of pi than Carlos memorizedEasyGSM8K
18848In a two-digit number, the digit in the unit's place is four…MediumAQuA
18894How many positive 5-digit integers have the odd sum E of their…MediumAQuA
18910A and B are playing mathematical puzzlesMediumAQuA
18916Each digit in the two-digit number G is halved to form a…MediumAQuA
18920The security gate at a storage facility requires a Six-digit lock codeMediumAQuA
19047If the sum of 1/3 and 22/99 is converted to a decimal…MediumAQuA
19318How many odd 4-digit positive integers T that are multiples of 5…MediumAQuA
19348How many three digit number can be formed with the numbers 1,2,3,4,5MediumAQuA
19509How many six-digit numbers are there such that all six digits are…MediumAQuA
19572If 16^5*15^4*14^3*13^2 = x, what is the units digit of x MediumAQuA
19585How many three digits number can be formed by using the digits…MediumAQuA
19650A and B are positive two-digit integers such that the tens digit…MediumAQuA
19655Three distinct single-digit numbersMediumAQuA
20059What will be in unit's place digit of 3 to the power…MediumAQuA
20217Find a two digit number, given that the sum of the digits…MediumAQuA
20235The addition 742586 + 829430 = 1212016 is incorrectMediumAQuA
20268How many positive 5-digit integers have the odd sum R of their…MediumAQuA
20270What is the 4 digit number in which the 1st digit is…MediumAQuA
20292The number obtained by interchanging the two digits of a two digit…MediumAQuA
20464What digit appears in the units place in the number obtained when…MediumAQuA
20554The unit digit in the product (611 * 704 * 912 *…MediumAQuA
20812How many 4-digit positive integers are there, where each digit is positive…MediumAQuA
20858The first three terms of an infinite sequence are 2, 7, and…MediumAQuA
20936A 5-digit code consists of one number digit chosen from 1, 2…MediumAQuA
21007How many 4-digit positive integers are multiple of each integer from 1…MediumAQuA
21116All of the citizens of a country have a three-character or four-character…MediumAQuA
211358+88+888+.....+8888........8888MediumAQuA
21156A boy multiplied 987 by a certain number and obtained 559981 as…MediumAQuA
21167How many integers n greater than and less than 100 are there…MediumAQuA
21197If d is a positive integer, and if the units' digit of…MediumAQuA
21201How many four digit even numbers do not use any digit more…MediumAQuA
21239S is the infinite sequence S1 = 2, S2 = 22, S3…MediumAQuA
21259The standard serial numbers for a bill are 2 letters followed by…MediumAQuA
21481S is the infinite sequence S1 = 2, S2 = 22, S3…MediumAQuA
21485Of the seven-digit positive integers that have no digits equal to zero…MediumAQuA
21489The difference between a two-digit number and the number obtained by interchanging…MediumAQuA
21510Find the last digit of 1!+2!+3!+4!+...............100MediumAQuA
21606What is the thousandths digit in the decimal equivalent of 57/5000MediumAQuA
21702The integer E has a tens digit of 6 and a units…MediumAQuA
21773How many four digit numbers can be formed using the digits {1…MediumAQuA
21803Yid intended to type a seven-digit number, but the two 3's he…MediumAQuA
21808The tens digit of a two-digit number is two more than its…MediumAQuA
21811Let x and y be positive integers, and r and s be…MediumAQuA
21823Meena wrote all the numbers from 1 to 49,999 inclusiveMediumAQuA
21832If in a given number 5 8 9 4 3 2 7…MediumAQuA
21856A warehouse is labeling computer inventory with 5-digit codesMediumAQuA
21891How many odd three-digit integers greater than 800 are there such that…MediumAQuA
22048Let a, b, c be distinct digitsMediumAQuA
22145How many odd 4-digit positive integers E that are multiples of 5…MediumAQuA
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