Brain-Teaser 19: Hillside Farm
From The Sunday Times, 9th July 1961 [link]
My friend, Mr. Little, is a farmer whose chief interest is in sheep, but keeps a number of Shorthorn and Redpoll (polled) cattle too.
Mr. Little is six years older than his wife and 33 years older than his son, George. George is twice as old as Mary, the daughter of the house, whose birthday happens to be today.
There is no tractor at Hillside Farm and Mr. Little does the ploughing behind his two horses leaving a furrow nine inches wide. The number of acres ploughed this year happens to be the same as the number of cats on the farm.
Readers are invited to determine the information required to complete the following “cross-number” puzzle:
Across:
1a: Number of Mr. Little’s Redpoll cows.
3a: Square of the number of Redpoll cows.
5a: Total number of cows.
6a: Mr. Little’s age.
7a: Number of ewes per ram in Mr. Little’s flock. This also happens to be the number of miles walked by Mr. Little in doing this year’s ploughing.
9a: Acreage of rough grass land. (1.5 acres per ewe).
11a: Age of Mrs. Little.
12a: Number of ewes in flock (in scores).
13a: Cube of the number of collies on the farm.Down:
1d: Area of rectangular farmyard in square yards.
2d: Length of farmyard in yards.
3d: Number of ewes on the farm.
4d: Age at which Mr. Little intends to retire.
7d: Seven times Mr. Little’s age.
8d: Total number of sheep.
10d: Number of rams on the farm.
12d: Total number of horns possessed by all the cattle.
[teaser19]
Frits and 
S2T2 
Jim Randell 10:12 am on 24 January 2021 Permalink |
I didn’t need to use all the information given to solve the puzzle. But I did need to look up what “polled” meant – it means “lacking horns”.
I used the [[
SubstitutedExpression]] solver from the enigma.py library to solve the puzzle as a collection of alphametic expressions.The following run file executes in 131ms.
Run: [ @repl.it ]
Solution: The completed grid looks like this:
From which we get the following information
And from the text we can deduce the following further information:
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Frits 2:06 pm on 24 January 2021 Permalink |
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Frits 6:12 pm on 24 January 2021 Permalink |
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from functools import reduce # convert numbers to digit sequences and vice versa # Credit: B. Gladman d2n = lambda s: reduce(lambda x, y: 10 * x + y, s) n2d = lambda n: [n] if n < 10 else n2d(n // 10) + [n % 10] # consider the grid: # # A B # C D E # F G # H I # # J # K L # M # N P Q R # S # # T U # V W # # # # X Y Z # "VW * 20 = CHLR" for V in range(1, 10): for W in range(10): CHLR = d2n([V, W]) * 20 if len(str(CHLR)) != 4: continue (C, H, L, R) = n2d(CHLR) # "AB * AB = CDE" for A in range(1, 10): for B in range(1, 10): AB = d2n([A, B]) CDE = AB * AB if len(str(CDE)) != 3: continue (c, D, E) = n2d(CDE) if c != C: continue # "2 * NPQR == 3 * CHLR" NPQR = int(1.5 * (CHLR)) if len(str(NPQR)) != 4: continue (N, P, Q, r) = n2d(NPQR) if r != R: continue # "PT * KL = CHLR" for K in range(1, 10): PT = CHLR // d2n([K, L]) if len(str(PT)) != 2: continue (p, T) = n2d(PT) if p != P: continue # "CHLR + PT = MSWZ" MSWZ = CHLR + PT if len(str(MSWZ)) != 4: continue (M, S, W, Z) = n2d(MSWZ) # "2 * (FG - AB) = VY" for Y in range(10): FG = AB + d2n([V, Y]) // 2 if len(str(FG)) != 2: continue (F, G) = n2d(FG) # "TU + 6 = HI" for U in range(10): HI = d2n([T, U]) + 6 if len(str(HI)) != 2: continue (h, I) = n2d(HI) if h != H: continue # "HI < DI" if not HI < d2n([D, I]): continue # "HI * 7 = KQU" KQU = HI * 7 if len(str(KQU)) != 3: continue (k, q, u) = n2d(KQU) if k != K or q != Q or u != U: continue # "is_cube(XYZ)" for X in [1, 2, 3, 5, 7]: XYZ = d2n([X, Y, Z]) if not XYZ in {125, 216, 343, 512, 729}: continue # "AFJN % BG = 0" for J in range(10): AFJN = d2n([A, F, J, N]) if not AFJN % d2n([B, G]) == 0: continue print("CHLR CDE AB PT FG HI KQU MSWZ XYZ") print(CHLR, CDE, AB, PT, FG, HI, KQU, MSWZ, XYZ) print("A B C D E F G H I J K L") print(A, B, C, D, E, F, G, H, I, J, K, L) print("M N P Q R S T U V W X Z") print(M, N, P, Q, R, S, T, U, V, W, X, Z)LikeLike