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VTMO 2026 - Grade 7 - Final - SET 8 - Self-study Question 5

VTMO · VTMO 2026 - Grade 7 - Final - SET 8 - Self-study

Question 5

Four players $A,B,C,D$ each wear a shirt numbered 6, 7, or 8. A player wearing 7 always lies; a player wearing 6 or 8 always tells the truth. Asked for the sum of all four shirt numbers, they reply:

$A$: “The sum is 28.”

$B$: “The sum is 27.”

$C$: “The sum is 26.”

$D$: “The sum is 25.”

Find every player’s shirt number. Give the ordered tuple $(A,B,C,D)$.