Given: $ Y $ is a pan-digital number (a number containing every digit from 1 to 9 exactly once) ending in 3 Without using computers or calculators, find $ X $: $$ Y = (X - 1)^5 + (X + 7)^5 + (2X + 6)^5 + (4X + 3)^5 + (5X + 8)^5 $$ Most concise, logical answer will be accepted.

In our Reptand prime family, as you know, everybody has our own signature Rep unit. My younger sibling unit has shorter repunit and he wanted to create little puzzle for you. He truncated his repunit to five digits. He says if you place 1 at the end of truncated unit, it becomes 3 times larger t...

Q1: 000，X00，？，XX0 ，X00 Q2: 6X000X9，700XX08，00000015，？，00000015，？，00000015 These two alphametic questions actually come from the puzzles made by my friend. He gave me his puzzles recently but I couldn't figure it out. Any clues? Hint1 Hint2 Hint3

Somebody has messed up my bookshelf by shoving a book into completely the wrong place. Which is the intruder?

After pressing the button, the walls opened. This time, instead of a damp smelly room, a futuristic lab appeared. "What the-" exclaimed Cyrus. T.E.D. scanned the whole lab quickly. Cyrus couldn't believe what he saw, since he was exploring ruins inside a deep forest. However, he could onl...

This puzzle is part 12 of Gladys' journey across the globe. Each part can be solved independently. Nevertheless, if you are new to the series, feel free to start at the beginning: Introducing Gladys. Dear Puzzling, A new day, a new city. Once again, there is so much to see...

I want to share a question that is created by myself. I will give a hint in 24 hours and my answer in 3 days given that nobody could answer my question. Here is my number sequence: 3/2,2/3,3/4,1/3,3/8,?

All but nine of the clues are normal. The remaining nine are printer's devilry clues, whose answers are thematic. Solvers must fill the grid correctly and use the thematic material to identify an appropriate location. All answers (except thematic ones) may be found in Chambers dictionary, as m...

When looking through the two tags descriptions and related questions, to me they seem to fall under the same category. They both set up a seemingly normal situation with some twist that requires outside the box thinking to come to the unique correct answer. Should lateral-thinking & situation be...

New here so apologies if this is not quite allowed. Yesterday our department had a meeting in one of our conference rooms on campus. When we arrived the room was empty, but there were three puzzles written on three panels of the whiteboard. Two of them were fairly straightforward number sequences...

Can you arrange a standard set of $28$ dominoes into a rectangle of $7\times8$, where each of the 8 rows sum to $21$ and each of the 7 columns sum to $28$? Image from WikiPedia. The 'twistier' the better!

I can break you, Or take you, And captivate you forever. I strike you, In moments where you’re weak. I strike you so that Forget me you will never. This arrow pierces you deep and sound. Come get me before your life runs aground. What am I?

The river, a cycle. The symbol, a part. The node, an object. One word. Hint:

Given: A, B, C are all primes Find the smallest composite number Y that satisfies the relation: $ Y = A ^ C + B ^ B + C ^ A $