Million Bank Balance Puzzle (MPMP Puzzle 6)

Puzzle Video

A bank is running a competition. You can make two deposits (of integer pounds) on two consecutive days and everyday the bank will add your last two balances together to give you a new balance.

For example: You deposit £10 on day 1 and £20 on day 2. Your balance on day 1 would be £10, day 2 £30, day 3 £40, day 4 £70 and so on.....

You can keep the money if your balance eventually equals one million pounds exactly. If more than one person hits a million exactly, the prize goes to the person who took the longest to get there. 

Puzzle for Submission: What must your initial two deposits be to ensure that you win the million pounds? 

Solution Video