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What are cyclic numbers?
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What are cyclic numbers?

Cyclic numbers are those that multiplied by another number less than or equal to the number of digits that it has, their numbers will be repeated cyclically, passing to the end those in front. For example: The first cyclic number is 142857. If this number (which has six digits) is multiplied by the numbers from 1 to 6 we get: 2 x 142857 = 285714 (note that 1 and 4 were passed to the end) 3 x 142857 = 428571 (1 goes to the end ) 4 x 142857 = 571428 5 x 142857 = 714285 6 x 142857 = 857142 If we multiply by 7 what we get is 999999.

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Challenge 129

Take 4 out of 4 and left 8 Difficulty Level: How to take out 4 out of 4 so that over 8? Challenge 128 Nine Challenge Challenge Index Next >> Challenge 130 The Traveler
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Challenge 133

The Merchant and the T-shirts Difficulty Level: A merchant bought some t-shirts for $ 720 and sold them for $ 65 each, earning the cost price of one of them on the sale of all t-shirts. What was the cost price of each t-shirt? Challenge 132 Adults and Children in Elevator Challenge Index Next >> Challenge 134 Nephew's Mother Sister…
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Challenge 139

Olive in the bowl Difficulty level: The four sticks in the figure below represent a bowl. You should move the olive from the bowl to a new position by moving only two sticks. But you cannot touch the olive and must keep the exact shape of the bowl. Challenge 138 Five-digit number Challenge index Next >> Challenge 140 The next word
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Challenge 108

The rooms and lamps Difficulty level: Two rooms are connected by a corridor. In the first room there are three lamps (a, b and c) which are connected to three switches (1, 2 and 3) located in the second room. How to know which switch corresponds to each lamp having only one opportunity to move from one room to another?
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Challenge 105

Moving only one toothpick Difficulty Level: Move only one toothpick to form a square. Challenge 104 Clodovando's father and grandfather Challenge table of contents Next >> Challenge 106 Radigunda needs money
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Challenge 156

Completing the sequence Difficulty level: What is the next number in the sequence? 1, 2, 6, 42, 1806,… Challenge 155 Sum of Two Cousins ​​Challenge Index Next >> Challenge 157 The Multiple of 9
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Challenge 146

The Five Sailors Difficulty Level: You are the captain of a ship. Five sailors stand before him to receive his orders. Try naming them from left to right according to the information: - Anderson is between Jorge and Claudio; - Humberto is on Claudio's left; - Jorge is not beside Humberto; - Humberto is not next to Rafael.
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Challenge 170

The square that starts at 999 Difficulty Level: What is the smallest natural number whose writing in your square starts at 999? Challenge 169 Playing Dice Challenge Table of Contents Next >> Challenge 171 The False Cube Unfolded
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Challenge 159

Joaozinho waiting for buses Difficulty level: Joaozinho observed that in his neighborhood the bus lines run 24 hours a day and that the bus runs in the Gama neighborhood of Alfa city every 6 minutes. Joaozinho also knows that at the stop where he usually stays, a bus goes at exactly 1:46 pm.
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Challenge 15

Check Filling Error Difficulty Level: One person, when writing a check, reversed the tens to hundreds. Therefore, overpaid the amount of $ 270.00. Knowing that the two digits are as one is to two, calculate the figure on the check, which was written in the tens.
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Challenge 163

The Cat, the Coffee, and the Cake Difficulty Level: Ten minutes before putting the cake in the oven, I put my cat outside the house. The cake should cook for 35 minutes, so I set the alarm clock to ring at 35 minutes after placing the cake in the oven. I immediately made myself a coffee, which took me 6 minutes.
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Challenge 171

The False Unfolded Cube Difficulty Level: The following are five possible versions of an unfolded cube. One of them is impossible. What? Challenge 170 The Square Starting at 999 Challenge Table Next >> Challenge 172 Planting a Flower
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Challenge 178

Letters and Envelopes Difficulty Level: While watching television, Romiscleison placed three letters in three separate envelopes, all addressed to different locations. He paid no attention to which letter was placed in each envelope. What is the chance of each letter being in the correct envelope? Challenge 177 Cracking a Barcode Challenge Index Next >> Challenge 179 Secret Operation
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Challenge 181

Adding Six Difficulty Level: Using positive integers, how many different ways can you make a sum that equals 6? For example, you could use: 1 + 2 + 3 = 6 3 + 1 + 1 + 1 = 6 and so on. Note: Consider 4 + 2 to be the same as 2 + 4. Challenge 180 The Beggar and the Cigarettes Challenge Index Next >> Challenge 182 Move a Toothpick
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Challenge 29

The number 1234512345123451234512345 Difficulty level: Cut 10 digits from the number 1234512345123451234512345 so that the remaining number is as large as possible. Challenge 28 Possible values ​​for x? Challenges Index Next >> Challenge 30 Find 2 3-digit numbers…
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Challenge 190

Boy, girl and dog Difficulty level: A boy, a girl and a dog are weighed on a scale in three ways, as shown in the figure. How much would the three together weigh? Challenge 189 Fourth power plus four Challenge table Next >> Challenge 191 The boy, the sneakers and the whistles
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Challenge 19

Form Number 24 Difficulty Level: Form number 24 using only numbers 3, 3, 7, 7 once each. You can use the +, -, *, / operations as well as parentheses if you find it necessary. Challenge 18 Balls on the Straight Challenge Index Next >> Challenge 20 Root Larger Than Number
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Challenge 187

Which fits you best? Difficulty Level: Which fits you best? A round piece in a square hole or a square piece in a round hole? Challenge 186 Investigating the Sequence Challenge Index Next >> Challenge 188 Climbing the Steps
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Challenge 2

Combinatorial analysis Level of difficulty: A car holds two passengers in the front seat and three in the rear seat. Calculate the number of different alternatives to fill the car using 7 people, so that one of these people never occupies a front seat seat. Challenge 1 The Age Problem Challenge Index Next >> Challenge 3 Age Ratio
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Challenge 55

The Bridge Difficulty Level: 4 friends must cross a flimsy wooden bridge at night, and it is essential to use a flashlight to cross. The bridge can only support the weight of 2 people and friends have only one flashlight. Camila takes 8 minutes to cross, Manolito takes 4 minutes, Carlos takes 2 and Romerito 1 minute.
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