The remains of GAMES

Number Theory Level 3

G A M E S ÷ G \textcolor{#D61F06}GAMES\div \textcolor{#D61F06}G leaves remainder 1.
G A M E S ÷ A G\textcolor{#3D99F6}AMES\div \textcolor{#3D99F6}A leaves remainder 2.
G A M E S ÷ M GA\textcolor{#20A900}MES\div \textcolor{#20A900}M leaves remainder 3.
G A M E S ÷ E GAM\textcolor{#69047E}ES\div \textcolor{#69047E}E leaves remainder 4.
G A M E S ÷ S GAME\textcolor{#EC7300}S\div \textcolor{#EC7300}S leaves remainder 5.

Replacing each letter with a distinct digit, what is the 5-digit number GAMES ?


The answer is 23459.

Ronald Chén by Ronald Chén , 32, Guatemala

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1 solution

Giorgos K.
Feb 22, 2018

Mathematica

Select[Permutations[Range@9, {5}],Table[Mod[FromDigits@#,#[[k]]],{k,5}]==Range@5&]

returns {{2, 3, 4, 5, 9}}

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