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Binary Decimal (Posted on 2024-05-27)

Determine the smallest integer N such that the decimal representation of N contains only the digits 0 and 1, and there are 8 distinct integers A,B,C,D,E,F,G,H where the 8 quotients N/A, N/B, N/C, ..., N/H are all pandigital integers.

That is, each quotient contains each of the digits 0 to 9 exactly once. For example, 1001100111111 / 373 = 2683914507.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

The smallest value of N is 111111110100000. The respective values of A to H are as follows:
A=11250=> N/A = 9876543120 B= 18000 => N/B = 6172839450 C= 22500 => N/C = 4938271560 D= 28125 => N/D = 3950617248 E= 36000 => N/E = 3086419725 F= 45000 => N/F = 2469135780 G= 56250 => N/G = 1975308624 H= 90000 => N/H = 1234567890
It is observed that each of the values of N/A, N/B,......,N/G, N/H is a 10-digit pandigital number.
For an explanation, refer to the solution submitted by Charlie in this location.

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	Subject	Author	Date
	computer solution	Charlie	2024-05-27 14:00:22

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