# Modulo - practice problems

#### Number of problems found: 24

- A labourer

A laborer who works five days a week starts working on Monday at 10 am. If he works for 56 days, on which day will he complete the job? - Market open

A certain market opens for sales every 7th day of the week. If it opened last on a Friday, on what day of the week will the market be opened again after nine months? (Hint: a month is 30 days) - Fraction to decimal infinite

Find which digit is at 1000th place after the decimal point in the decimal expansion of the fraction 9/28. - Quarter of an hour

If the clock showed a quarter of an hour more, it would be 10 minutes to 10 hours. How many hours do they show? - Remainder 34441

Find the remainder after division when we divide the sum of 1! +2! +3! +. ... . +300! number 13. - Yesterday 13711

If the day before yesterday was what day of the week it will be from today in 50 days. (0 = Monday, 6 = Sunday) - Twos

Vojta started writing the number this year, 2019202020192020, into the workbook. And so he kept going. When he wrote 2020 digits, he no longer enjoyed it. How many twos did he write? - Justification 8468

The natural number n has at least 73 two-digit divisors. Prove that one of them is the number 60. Also, give an example of the number n, which has exactly 73 double-digit divisors, including a proper justification. - Restriction 7442

The figure shows two rows of hexagonal boxes that continue to the right without restriction. Fill in one field with one positive integer so that the product of the numbers in any three adjacent fields is 2018. Determine the number that will be in the top - Electricity 7115

On Tuesday at 6 o'clock, the electricity supply was interrupted at 156 h. On which day (1 = Monday, ... 7 = Sunday) and at what time was the electricity supply resumed? - Big number

What is the remainder when dividing 10 by 9 to 47 - 111? - Christmas

Father said: "exactly after 56 hours, we will sit down at the Christmas Eve table" How was it and what time was it when Father said this sentence? They sit at the Christmas Eve table at exactly 6 PM. - Modulo

Find x in the modulo equation: 47x = 4 (mod 9) Hint - read as what number 47x divided by 9 (modulo 9) give remainder 4. - Organizes 4152

Bača has less than 500 sheep. If he organizes them in 4 rows, he will have three sheep. If he organizes them in 5 rows, he will have four sheep; and if he arranges them in 6 rows, he will have five sheep. But it can manage them exactly in 7 rows. - Grandmother's clocks

Grandmother's clock is late every hour by half a minute. Grandmother set the clock exactly at 8.00 am. How many hours will show after 24 hours? - Clock hands

The hands-on clock shows the time of 12 hours and 2 minutes. Calculate the size of an acute angle between clock hands three hours later. - Christmas

Exactly after 114 hours, we sit down at the Christmas Eve table. What day and what time was it when Dad said this sentence? They sit at the Christmas Eve table exactly at the 18-o'clock (6 pm). - Remainders

It is given a set of numbers { 170; 244; 299; 333; 351; 391; 423; 644 }. Divide these numbers by number 66 and determine a set of remainders. As a result, write the sum of these remainders. - Sweets

Mom bought a box of sweets for their children. The whole package of 137 sweets is divided among 5 their children so that each child receives the most and for she remains the least sweets. How many sweets are left for mom? - Clock

How many times a day do hands on a clock overlap?

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