Sunday Times Teaser 3261 – The Evidence of Weight
by Stephen Hogg
Published Sunday March 23 2025 (link)
The sunbathing pontoon’s four identical, cubic, sealed floats had widths a whole number of centimetres (less than 100). Arkim, Edie’s son, knew that the pontoon’s labelled weight of 20,000 grams would equal the combined submerged volume of the floats in cubic centimetres, if the pool water’s density was one gram per cubic centimetre.
Later, with Edie alone on the pontoon (once again level in still water), the floats were a whole number of centimetres further partially submerged. Assuming the above, Arkim calculated Edie’s weight to be a whole number of kilograms (under her 90kg peak, but above her 50kg “wedding” weight).
If I were a cad and revealed Edie’s weight, you would be unsure of a float’s width.
Give Edie’s weight in kilograms
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BRG permalink123456789101112131415161718192021222324# Edie's weight <W>Kg (integer), float width <w> (integer), incremental# float depth <h> (integer) ==> 10^3.W = 4.w^2.h ==> w = 5.sqrt(10.W / h)# hence w is a multiple of 5# initial float depth <d> such that 4.w^2.d = 2.10^4 ==> d = 2.(50 / w)^2# collect solutions indexed on Edie's weightW2s = {}# consider the float width <w>for w in range(5, 100, 5):# calculate the initial float depth <d>d = 2 * (50 / w) ** 2# added depth <h> with Edie's weight W = 4.w^2.hfor h in range(1, w - int(d) + 1):# Edie's weight in kilogramsW, r = divmod(4 * w * w * h, 1000)if not r and 50 < W < 90:W2s[W] = W2s.get(W, set()) | {(w, d, h)}for W, s_wdh in W2s.items():if len(s_wdh) > 1:print(f"Edie's weight is {W}Kg.")
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GeoffR permalink12345678910111213141516171819202122232425from collections import defaultdictwt = defaultdict(list)for w in range(5, 100, 5):# calculate submerged depth due to Edie's weightfor d2 in range(1, 100):E = 4 * w * w * d2if E % 1000 == 0:if not (50000 < E < 90000):continue# calculate submerged depth due to self weightd1 = round(5000 / w ** 2, 4)if d1 + d2 > w:continue# update dictionarywt[E] += [(E // 1000, w, d1, d2)]# Look for more than one solutionfor k, v in wt.items():if len(v) > 1:print(f"Edie's Weight = {v[0][0]} kg.")print(v)
