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#61 Triple jump

鈥淢y Auntie Connie just had triplets, three boys!鈥濃�漌ow, how old is she?鈥濃�滻 dunno, but she鈥檚 really old.鈥濃�滵o you think the boys鈥� ages will ever catch up to your auntie鈥檚? If you add all three together, I mean.鈥�

鈥淚鈥檓 not sure they鈥檒l ever add up to her age exactly 鈥� I think it depends on how old she is now.鈥�

Assuming they all live to a ripe old age, what are the chances that there will come a date in the future when the ages of the three boys add up exactly to their mother鈥檚 age? (To be clear: your 鈥渁ge鈥� is how old you were on your last birthday, so it is always a whole number.)

Answer next week

#60 Mexican standoff

Solution

Bumbling has a 78 per cent chance of surviving. The best strategy for each shooter is to take out their strongest rival first, so Good should aim first at Bad, while Bad and Bumbling should aim at Good.

The chance that Bad will get through the first round is only 1 per cent, so we will be close to the right answer if we call that zero. Good only survives if Bad and Bumbling both miss him, 0.33 x 0.66 = 0.22, or a 22 per cent chance. If Good does survive, he is almost certain to kill Bumbling in the second round.

Therefore the chance that Bumbling will survive is 100 鈥� 22 = 78 per cent. The 1 per cent chance of Good missing Bad slightly lowers Bumbling鈥檚 chances of survival.