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#67 Pandigital sums

Set by Colin Beveridge

A pandigital sum is an addition that uses each of the digits from 0 to 9 exactly once, and no number within the sum starts with a zero. For example, 4927 + 86 = 5013 can be represented as ABCD + EF = GHIJ, where each letter is a different digit.

There are 36 pandigital sums of the form ABCD + EF = GHIJ. Can you find one where GHIJ = 2034?

There are 96 pandigital sums of the form ABC + DEF = GHIJ. How many can you find where GHIJ = 1089?

There is one pandigital sum of the form ABC + DEF = GHIJ where A < B < C < D < E < F. Can you find it?

Solution next week

#66 Easy times?

Solution

To get from 15 to 51, multiply 15 by 3.4.

135 × 2.6 = 351. Moving a digit from the front to the back is the same as multiplying the smaller number by 10, subtracting 1000 and adding 1, so we can write 10n – 1000 + 1 = 2.6n, where n is the number you are moving a digit of, and solve this equation.

12,195 × 1.8 = 21,951. Here, a similar formula is used, but instead of 1000, we subtract 100,000.

123,456,790 × 1.9 = 234,567,901.

In general, if n is a d-digit number, with f as the first digit, then moving its first digit to the opposite end gives the number 10n – (f × 10d) + f = m × n, where m is a suitably chosen multiplier.