Enigma: No. 832: Big tax has little taxes

22 July 1995

The country in which Uncle Fibo at present resides has introduced a peculiar new tax system. It is based on the following principles:

1: All taxable income is taxed at a “basic tax rate”.

2: On all taxes payed, a rebate is given, calculated at the basic tax rate.

3: All tax rebates are treated as taxable income.


Uncle Fibo has calculated that, at the basic tax rate applicable to him, the effective tax which he has to pay would be the same if he paid his entire taxable income for a given period over to the taxman and then received back from him a once-off non-taxable rebate on this amount, calculated at the basic tax rate.

What is Uncle Fibo’s basic tax rate, given to the nearest tenth of a percentage point?

A £10 book token will be awarded to the sender of the first correct answer opened on Thursday 24 August. The Editor’s decision is final. Please send entries to Enigma 832, New Scientist, King’s Reach Tower, Stamford Street, London SE99 0BB. The winner of Enigma 826 was R. Price of Preston, Lancashire.

Answer to Enigma 826


One square unit.