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Nine, Ten and One

Age 11 to 14 Short Challenge Level:
t = 5

We are given that 2n + e = 8 and t + e + n =10. Subtracting the first equation from the second gives t - n = 2.

As n cannot equal 1, the minimum value of t is 4 but this gives n = 2, e =4 which is not allowed.

If t = 5 then n = 3 and e = 2, which is allowed.

If t > 5 then n >3 and e is not a positive whole number, so 5 is the only possible value of t.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.