Sunday Times Teaser 3005 – Tubular Bales
by Stephen Hogg
Published Sunday April 26 2020 (link)
Ten equal-length, rigid tubes, each a different prime-valued external radius from 11mm to 43mm, were baled, broadside, by placing the 43mm and 11mm tube together and the third tube, not the largest remaining, touching both of these. Each subsequent tube touched the previous tube placed and the 43mm tube. A sub-millimetre gap between the final tube placed and the 11mm tube, made a near perfect fit.
The radius sum of the first three tubes placed against the 43mm tube was a multiple of one of the summed radii. Curiously, that statement remains true when each of “four”, “five”, “seven” and “eight” replaces “three”. For “two” and “six” tubes placed their radius sum was a multiple of an as yet unplaced tube’s radius.
What radius tube, in mm, was placed last?
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