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Can you find the missing number?

the brainbuster

This competition is now closed.

A straightforward poser this time:

What is the missing number X in the following sequence?

19  39  45  58  X  68  70

Show your reasoning.

the entries

Many thanks to all of you who entered the brainbuster.

Again this one attracted a good number of entries. Most entrants worked out the correct answer but some of the logic was clearer than others!

the solution

Here is the answer as provided by our winner:

The missing number is 62. Add the first and second digit of each in the sequence, ie 1+9=10, 3+9=12, 4+5=9, 5+8=13, MISSING, 6+8=14, 7+0=7. The difference between the sum for one of the numbers and the next in the sequence increases by one each time: 12-10=2, |9-12|=3, 13-9=4, ... |7-14|=7. This means that the difference between the 6+8=14, needs to be reduced by 6 to get the sum of the numbers of the missing two-digit number. 14-6=8, therefore the two digits making the missing number must add up to 8. Given the increasing patter in the numbers the only two-digit integer which fits this criterion is 62 (6+2=8).

and the winner is...

Congratulations to Lawrence Fsadni, who wins £200 of Firebox vouchers.

Lawrence is studying for his Masters in Physics at the University of Manchester.

Many thanks again to all entrants - do try the next brainbuster!