Enigma 1069: Time for elevenses
26 March 2018
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From New Scientist #2225, 12th February 2000 [link]
I have a cube. On each of its faces is a digit, the style of writing being rather like the display on a calculator. I hold the cube to look at one of its faces from the front and then, keeping the upper and lower faces horizontal, I swivel the cube around and note the digits which I see (all seemingly the right way up) and hence I read off a four-figure number which is divisible by eleven.
Now I repeat the process starting this time looking from the front at one of the faces which was horizontal in the previous manoeuvre. Once again I read off a four-figure number which is divisible by eleven.
Now I start again with the cube in exactly the same position as it was at the start of the first process. This time I keep the left-hand and right-hand faces vertical and I swivel the cube around. Once again I read a four-figure number which is divisible by eleven and also by three odd integers less than eleven.
What was that last four figure number?