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Answer to Q23

A small number of cards has been lost from a complete pack. If I deal among 5 people, 2 cards remain. If I deal among 3 people, 1 remain and if I deal among 2 people, 1 cards remain. How many cards are there?

We already know the range of number we are looking for, a number less than 52 (a complete pack of cards). This number must fulfil all these following conditions

1. When divided by 5 it must have a remainder of 2 (clue 1)

2. When divided by 3 it must have a remainder of 1 (clue 2)

3. When divided by 2 it must have a remainder of 1 (clue 3)

We can now find this number via trial and error, but let's first list out all numbers with remainder 2 when divided by 5 between 1 and 51

47, 42, 37, 32, 27, 22, 17, 12, and 7

Testing 47 with clue 2 and 3

Clue 2: 47 ÷ 3 = 15 Rem 2 (so 47 is not correct)

Testing 42 with clue 2 and 3

Clue 2: 42 ÷ 3 = 14 Rem 0 (so 42 is not correct)

Testing 37 with clue 2 and 3

Clue 2: 37 ÷ 3 = 12 Rem 1
Clue 3: 37 ÷ 3 = 18 Rem 1

Fulfilled all 3 clues!

Answer: 37

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Create: 2019-08-08
Last Update: 2025-07-12 11:33:41

Answer to Q23

A small number of cards has been lost from a complete pack. If I deal among 5 people, 2 cards remain. If I deal among 3 people, 1 remain and if I deal among 2 people, 1 cards remain. How many cards are there?

We already know the range of number we are looking for, a number less than 52 (a complete pack of cards). This number must fulfil all these following conditions

1. When divided by 5 it must have a remainder of 2 (clue 1)

2. When divided by 3 it must have a remainder of 1 (clue 2)

3. When divided by 2 it must have a remainder of 1 (clue 3)

We can now find this number via trial and error, but let's first list out all numbers with remainder 2 when divided by 5 between 1 and 51

47, 42, 37, 32, 27, 22, 17, 12, and 7

Testing 47 with clue 2 and 3

Clue 2: 47 ÷ 3 = 15 Rem 2 (so 47 is not correct)

Testing 42 with clue 2 and 3

Clue 2: 42 ÷ 3 = 14 Rem 0 (so 42 is not correct)

Testing 37 with clue 2 and 3

Clue 2: 37 ÷ 3 = 12 Rem 1
Clue 3: 37 ÷ 3 = 18 Rem 1

Fulfilled all 3 clues!

Answer: 37

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