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 A^2 = B^3 + C^3
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 smallest integer whose first n multiples all contain a 3
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 Set {2,b,c,d,e} such that the product of any two of them increased by 1 is a square
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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
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
#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 1/7th … 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 4digit number, abcd, then find N such that … Continue reading
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 2digit numbers. AB * AA ——— BAAB AB * AA = BAAB (10*A + B)(10*A + A) = 11*A*(10*A + B) = 110*A^2 + … Continue reading
Posted in Math Beauty
Tagged 4digit Num3ers, 5digit number, Digits, Digits Reversed
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Num3ers equal to 4th power to sum of its digits
(2 + 4 + 0 + 1)^4 = 2401 = 7^4 2 + 4 + 0 + 1 = 7 (2 + 3 + 4 + 2 + 5 + 6)^4 = 234256 … Continue reading
Cool Equalities – Same Digits, Digits 09
2digit numbers: Using all the digits 0 to 9 and the operations (+) and (), can you find a, b, c, d, e, f, g, h, i, j, such that ab ± cd ± ef … Continue reading