Mathematics
Look at the following pattern :
12 = 1
112 = 121
1112 = 12321
11112 = 1234321
111112 = 123454321
Make a conjecture about each of the following:
1111112 =
11111112 =
Check if your conjecture is true.
Mathematics Proofs
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Answer
Looking at above pattern,
Possible conjecture :
The resultant will be series of numbers from one till number of 1's in the digit to be squared and then reversing the order.
By following conjecture, we can write:
⇒ 1111112 = 12345654321 and
⇒ 11111112 = 1234567654321
On actual multiplication, we get :
⇒ 1111112 = 12345654321 and
⇒ 11111112 = 1234567654321.
Hence, conjecture is true.
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