August 2016

Going reverse!

Mohan was just scribbling away random four-digit numbers and multiplying them by 9. One particular four-digit number caught his attention. When he multiplied this number by 9, the result was again a four-digit number; curiously, the resulting number was reverse of the original number.

Let me elaborate on this so that you don't get me wrong. Suppose the original number was xyzw (x, y, z, w are not necessarily distinct), then upon multiplying xyzw by 9, the resulting number is wzyx. I can't give a true example because that will be giving away the answer; but, suppose the original number was 1234, then 1234 x 9 should give 4321. Of course, 1234 x 9 = 11106; now, 11106 is neither 4321 nor is it a four-digit number. So, 1234 is not the number Mohan hit upon.

Can you find the four-digit number which when multiplied by 9 yields a four-digit number as the result and which is the reverse of the original number?

Click here for the solution

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  • Birla Institute of Technology, Ranchi -
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  • Tata Institute of Social Sciences, Mumbai -

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