The times-11 trick on a three-digit number

Question

The eleven trick is not limited to two digits. Solve it in your head. What is 253 	imes 11? Aim: under 10 seconds.

Accepted Answer

Write the outer digits, then insert each running sum of adjacent digits: 2\ \underbrace{(2+5)}{7}\ \underbrace{(5+3)}{8}\ 3 = 2783. So 253 	imes 11 = \mathbf{2783}. Verify by shifting: 253 	imes 10 = 2530, plus 253 is 2530 + 253 = 2783. Correct. Watch for carries: if any neighbour-sum hit 10 or more, you would carry left. Here 2+5=7 and 5+3=8, both single digits, so it drops in cleanly. Takeaway. For any length, times-11 is "copy the ends, insert each adjacent-pair sum between." Just propagate carries when a pair sums to 10+.

The times-11 trick on a three-digit number

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