What woman could forget the unceasing friendship you and Nanda have shown us, dear Queen of Vraja? There is no way to repay you in this world, even with the wealth of Indra.

the number in the middle of each triple is the same as the digits of the number at either ends when added together.
e.g. 3+7=10=8+2

Soumil Shah
Ranch Hand

Joined: Jul 13, 2009
Posts: 54

posted

0

Here is another one...
There are four 3-digits natural numbers; each of them equals the sum of the cubes of its digits. Three of them are :
153=1+125+27
370=27+343+0
407=64+0+343

What is the fourth one? It does not begin with 0, otherwise it isn't 3-digit number.

Ulf Dittmer
Marshal

Joined: Mar 22, 2005
Posts: 42267

64

posted

0

Soumil Shah wrote:the number in the middle of each triple is the same as the digits of the number at either ends when added together.

4+2 = 11 ?

Ernest Friedman-Hill
author and iconoclast
Marshal

Simon Peter went up, and drew the net to land full of great fishes, an hundred and fifty and three: and for all there were so many, yet was not the net broken.

Soumil Shah wrote:Here is another one...
There are four 3-digits natural numbers; each of them equals the sum of the cubes of its digits. Three of them are :
153=1+125+27
370=27+343+0
407=64+0+343

What is the fourth one? It does not begin with 0, otherwise it isn't 3-digit number.

Once you know that one of the numbers in the list ends with a 0, it's obvious (for large values of obvious) that that number plus 1 should be on the list.

371

Can you find any four digit numbers that have this property?