Lemma

Number Theory · Chapter 7 of 11

Digits

21 curated · 993 from open sources

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AllEasyMediumDeep

Curated

21
#TitleDifficultySourceTags
593How long is 2¹⁰⁰?MediumLemmaDigits
1081Sum in base‑5MediumHall & Knightadditionbase conversion
1082Sum in base‑9MediumHall & Knightadditionbase conversion
1083Subtraction in base‑8MediumHall & Knightsubtractionbase conversion
1084Base‑12 subtractionMediumHall & Knightsubtractionbase conversion
1085Division after subtraction in base‑6MediumHall & Knightsubtractiondivision+1
1086Multiplication in base‑7MediumHall & Knightmultiplicationbase conversion
1093Division in base‑sevenMediumHall & Knightbase conversiondivision
1095Square root in duodecimalMediumHall & Knightbase conversionsquare root
1102Duodenary to decimalMediumHall & Knightbase conversionpositional notation
1103Base‑12 to base‑11MediumHall & Knightbase conversionpositional notation
1104Senary to nonaryMediumHall & Knightbase conversionpositional notation
1105Base‑9 to base‑8MediumHall & Knightbase conversionpositional notation
1113Base for fraction 25/128 as 0.0302MediumHall & Knightbase conversionfraction representation
1114Radix where 554 is 24²MediumHall & Knightbase conversionquadratic equation
1115Base for 511197 as 1746335MediumHall & Knightbase conversionpolynomial evaluation
1117Base for geometric fractionsMediumHall & Knightradixgeometric progression
1118Changing base representationMediumHall & Knightbase conversionequality of values
1122Binary weights for a tonMediumHall & Knightbinary representationweights
1508GCM in base‑sixMediumHall & KnightGCDbase arithmetic
1787Digits in different scalesMediumHall & KnightBase representationDiophantine equations

From open sources

993

Complete problems only, with worked solutions first. Show everything

#TitleDifficulty
18848In a two-digit number, the digit in the unit's place is four…Medium
18894How many positive 5-digit integers have the odd sum E of their…Medium
18910A and B are playing mathematical puzzlesMedium
18916Each digit in the two-digit number G is halved to form a…Medium
18920The security gate at a storage facility requires a Six-digit lock codeMedium
19047If the sum of 1/3 and 22/99 is converted to a decimal…Medium
19318How many odd 4-digit positive integers T that are multiples of 5…Medium
19348How many three digit number can be formed with the numbers 1,2,3,4,5Medium
19509How many six-digit numbers are there such that all six digits are…Medium
19572If 16^5*15^4*14^3*13^2 = x, what is the units digit of x Medium
19585How many three digits number can be formed by using the digits…Medium
19650A and B are positive two-digit integers such that the tens digit…Medium
19655Three distinct single-digit numbersMedium
20059What will be in unit's place digit of 3 to the power…Medium
20217Find a two digit number, given that the sum of the digits…Medium
20235The addition 742586 + 829430 = 1212016 is incorrectMedium
20268How many positive 5-digit integers have the odd sum R of their…Medium
20270What is the 4 digit number in which the 1st digit is…Medium
20292The number obtained by interchanging the two digits of a two digit…Medium
20464What digit appears in the units place in the number obtained when…Medium
20554The unit digit in the product (611 * 704 * 912 *…Medium
20812How many 4-digit positive integers are there, where each digit is positive…Medium
20858The first three terms of an infinite sequence are 2, 7, and…Medium
20936A 5-digit code consists of one number digit chosen from 1, 2…Medium
21007How many 4-digit positive integers are multiple of each integer from 1…Medium
21116All of the citizens of a country have a three-character or four-character…Medium
211358+88+888+.....+8888........8888Medium
21156A boy multiplied 987 by a certain number and obtained 559981 as…Medium
21167How many integers n greater than and less than 100 are there…Medium
21197If d is a positive integer, and if the units' digit of…Medium
21201How many four digit even numbers do not use any digit more…Medium
21239S is the infinite sequence S1 = 2, S2 = 22, S3…Medium
21259The standard serial numbers for a bill are 2 letters followed by…Medium
21481S is the infinite sequence S1 = 2, S2 = 22, S3…Medium
21485Of the seven-digit positive integers that have no digits equal to zero…Medium
21489The difference between a two-digit number and the number obtained by interchanging…Medium
21510Find the last digit of 1!+2!+3!+4!+...............100Medium
21606What is the thousandths digit in the decimal equivalent of 57/5000Medium
21702The integer E has a tens digit of 6 and a units…Medium
21773How many four digit numbers can be formed using the digits {1…Medium
21803Yid intended to type a seven-digit number, but the two 3's he…Medium
21808The tens digit of a two-digit number is two more than its…Medium
21811Let x and y be positive integers, and r and s be…Medium
21823Meena wrote all the numbers from 1 to 49,999 inclusiveMedium
21832If in a given number 5 8 9 4 3 2 7…Medium
21856A warehouse is labeling computer inventory with 5-digit codesMedium
21891How many odd three-digit integers greater than 800 are there such that…Medium
22048Let a, b, c be distinct digitsMedium
22145How many odd 4-digit positive integers E that are multiples of 5…Medium
22302Since 2001, the standard serial numbers on a New York state license…Medium
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