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Three digit numbers in which the middle one is a perfect squar

Question

Three digit numbers in which the middle one is a perfect square are formed using the digits $1$ to $9$ . Their sum is

134055

270540

170055

270504

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Three digit numbers in which the middle one is a perfect square are formed using the digits

1

9

. Their sum is

13 mins ago

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13 mins ago

Text solutionVerified

Let

A BC

be the number

A ϵ {1, 2, 3.....9}

B ϵ {1, 4, 9}

C ϵ {0, 1, 2, .....9}

Each possible choice for

B

occurs.

81

times

[9 \times 9]

Each possible choice for

A

C

occurs

27

times

[3 \times 9]

∴

Sum of all numbers

= 27 \times 100 \times (1 + 2 + 3 + ..... + 9) + 81 \times 10 (1 + 4 + 9) + 27 \times 1 \times (1 + 2 + 3.....9)

= 27 \times 45 \times 100 + 81 \times 10 \times 14 + 27 \times 1 \times 45

= 134055

Hence, this is the answer.

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Question Text	Three digit numbers in which the middle one is a perfect square are formed using the digits $1$ to $9$ . Their sum is
Answer Type	Text solution:1
Upvotes	150