Multiplying 1s Pattern

Algebra Level 1

$\begin{aligned} 11\times11 &=& 121 \\ 111 \times111 &=& 12321 \\ 11111 \times11111 &=& \, ? \end{aligned}$

123454321 12345654321 123546321 12344321

1 solution

Kay Xspre
Jan 18, 2016

We can make a multiplication from the outset, but we can also use mathematical induction which, in this case, is quicker. The first line, the amount of $1$ in square is two digits, hence the square being from 1 to 2 then reverse (without repetition of 2) to 1. Similarly, in the second line, the amount of $1$ in square is three digits, hence the square being from 1 to 3 then reverse (without repetition of 3) to 1.

Hence, the amount of $1$ in square is five digits, hence the square being from 1 to 5 then reverse (without repetition of 5) to 1, or by spelling out, $123454321$

De kita ne..

Abuzor Gifary - 5 years, 4 months ago

Multiplying 1s Pattern

1 solution

0 pending reports