Brain-Teaser 252: Blocks
From The Sunday Times, 27th February 1966 [link]
“See these eleven blocks?”, says a so-called friend. “Four of them of 8 inch thickness, two of them of 4 inch thickness, three of 3 inch and two of 1 inch thickness”.
“Pile them in a column 51 inches high with a 3 inch block at the bottom so that, remaining in position, individual blocks or combinations of adjacent blocks can be used to measure every thickness in exact inches from 1 inch to 48 inches”.
In what order do they stand?
This puzzle was included in the book Sunday Times Brain Teasers (1974, edited by Ronald Postill).
There are now 790 Teaser puzzles available on the site. And this accounts for 25% of all the Teaser puzzles published (to date).
[teaser252]
S2T2 
Jim Randell 8:54 am on 4 December 2022 Permalink |
(See also: Teaser 119, Teaser 560).
This Python program performs an exhaustive search of all possible stacks of blocks.
It runs in 268ms.
Run: [ @replit ]
from enigma import (multiset, subsets, csum, irange, printf) # the blocks blocks = multiset.from_dict({8: 4, 4: 2, 3: 3, 1: 2}) assert blocks.sum() == 51 # extract a 3 block blocks.remove(3) # and consider possible arrangements of the remaining blocks for bs in subsets(blocks, size=len, select="mP", fn=list): bs.insert(0, 3) # find what thicknesses can be measured ts = set(b - a for (a, b) in subsets(csum(bs, empty=1), size=2)) # can we measure all values from 1 to 48 if all(x in ts for x in irange(1, 48)): printf("{bs}")Solution: The pile of blocks (bottom to top) is one of the following two sequences:
One being the reverse of the other.
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