# Tag Archives: Digits

## Digit puzzle – 9 and 10 distinct digits

(1) Find all integers     whose decimal representation consists of 9 distinct nonzero digits such that   (2) Do the same for integers   consisting of 10 distinct digits (leading zeros excluded) such that:       … Continue reading

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## Pattern of Digits – Multiplication

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## #puzzle : Digits — (Part 2)

(1) Determine the smallest positive integer   N   such that, if the digit   7   is written after it and the digit   2   in front of it, the result is   91   times   … Continue reading

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## #puzzle | moving and deleting digits – (Part 1)

(1) Find the smallest positive integer   N   with the following property: If the first digit of   N,   which is   9,   is moved to the end of the number, the resulting integer is   1/7-th … Continue reading

## Powers N^x; N= 2,…, 99 and x=2,…,10

Numbers   N = 2,   3,   …  ,99   and   x = 2, 3, …, 10   Here’s a partial list of powers of numbers N that can be expressed in terms of their digits. Please complete … Continue reading

## Num3ers equal to the product of its first 3 and last 3 digits

Find all numbers N, such that N is equal to the product of its first 3 and last 3 digits. For example, if   N   is a 4-digit number,   abcd,   then find   N   such that … Continue reading

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## Expressing Num3er 24 out of other num3ers

Given the number N = 24 construct out of several other numbers, by taking the numbers and performing the basic operations. For example, Making   24   out of …. (0, 0, 0, 0)          (0! + 0! + 0! … Continue reading

## AB * AA = BAAB and ABCD * 4 = DCBA

Let   AB   &   AA   be 2-digit numbers.       AB       * AA     ———-     BAAB     AB * AA = BAAB (10*A + B)(10*A + A) = 11*A*(10*A + B) = 110*A^2 + … Continue reading