Sunday Times Teaser 2890 – Squares on Cubes
by Andrew Skidmore
Published February 11 2018 (link)
Liam has a set of ten wooden cubes; each has a different number (from 1 to 10) painted on one face (the other five faces are blank). He has arranged them in a rectangular block with all numbers upright and facing outwards. Each vertical side of the block shows some numbers which can be read as a perfect square. No two squares have the same number of digits.
Which square must be present?
One Comment
Leave one →
-
Brian Gladman permalink1234567891011121314151617181920212223242526272829# Since there are eleven visible digits for four different length# squares, the lengths must be 1, 2, 3 and 5 digits; the '10' digit# sequence must occur in the 5 digit square since it doesn't appear# in any 1, 2 or 3 digit square.# The arrangement is a one high 2 by 5 rectangular block with single# digit cube faces (d), the 10 cube face and blank cube faces (s) in# one of these two sequencees reading left to right around the faces## (s d 10 d d) (s d) (s d d d s) (d d)# (s d d 10 d) (s d) (s d d d s) (d d)# consider all five digit squaresfor d in (str(x * x) for x in range(100, 317)):# find those that contain the '10' sequence, at most two# '1's and at most one of all other digitsif ('10' in d and d.count('1') <= 2and all(d.count(c) <= 1 for c in '234567890')):# now consider all combinations of 1, 2 and 3 digit squaresfor a in ('149'):for b in (str(x * x) for x in range(4, 10)):for c in (str(x * x) for x in range(11, 32)):# find a combination of squares with one of each digit# from two to nine inclusive together with two oness = a + b + c + dif s.count('1') == 2 and all(s.count(c) == 1 for c in '234567890'):print(a, b, c, d)
