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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
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Joined: Jul 13, 2009
Posts: 54

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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
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Joined: Mar 22, 2005
Posts: 42958

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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 ?

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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?