**Darrel Barnes – 2020 Teddy Rocks Maths Essay Competition Honourable Mention**

“Good morning, your Eminence – and the top of the morning to you. What a fine day it is to be sure, your Eminence. Shall we go through your diary for today?”

The words, the same today as every day at this same time, faintly made themselves heard in the far distance of the room. The cardinal raised a hand in acknowledgement, knowing it would take some time for his chaplain to stagger along one side of the study and then the other, holding onto the bookshelf for safety before reaching his desk. Why he never elected to tread the hypotenuse was a mystery beyond the cardinal’s comprehension.

His Eminence had been looking out of his study window, contemplating the early autumn day outside, and wondering what was the rate of growth of a Michaelmas daisy compared to a hollyhock, but gave up trying. “You need someone clever to work that one out”, he thought; “someone really clever. A botanist. Or perhaps a Director of Science at Kew.”

He looked on with a certain envy at a laughing gaggle of ordinands making their way across the quadrangle, past the well which had recently been gilded with uplifting spiritual words, to the library which was now housed in a redundant church. “Ah, ordinands in their prime – and here am I, a cardinal,” he mused, savouring the mathematical allusions.

He turned back to his desk which was now providing support for his chaplain. The cardinal could have sworn that the stench of Jameson’s on the young man’s breath had curled the petals of the cut flowers which had been freshly arranged in a small vase by his housekeeper that morning, but he pressed a handkerchief to his nose, and looked at the engagement diary which now lay open before him.

Leafing through the pages to find the correct day (his chaplain had mistaken September for December which was easy enough to do, considering that each day in September corresponded with exactly the same day three months later apart from New Year’s Eve – obviously) the cardinal ran swiftly through the appointments and then stopped abruptly.

“What’s this at 11:00 am? An hour’s prayer for Kirk Douglas? The actor? Good grief. Can’t you get anyone else to pray for him?” The cardinal fingered his pectoral cross in the fond hope that the crucified Christ might do the dirty work in his place.

“The bishop is busy sorting out transgender rights, your Eminence; oh, and historical child abuse, and he’d take three hours anyway”.

“Shorter than *Spartacus*, then,” joked the cardinal. “Your Eminence?”

“Never mind.”

“And, your Eminence,” the chaplain continued, “before you ask, the local monsignor is indisposed – coronavirus, I understand, contracted during his recent mission to bring spiritual comfort to cruise liner passengers on a visit to China and the Far East.”

“Friar Tuck?” asked the divine, angling the ruby on his ring in an attempt to dazzle the young man in front of him.

“Friar Tuck is occupied with Maid Marian, your Eminence. In any case, not possessing your Eminence’s 5G communications links to the Almighty, the monsignor and the friar would need five and seven hours respectively.”

“Fuck!” said the cardinal (to himself). “Very well: I’ll do it.”

The chaplain made a note in the diary, coughed and hesitated.

“Yes? What is it now?”

“Forgive me, your Eminence, but next week we have been asked to intercede for another late actor who is twice as much in need of intercession.”

“So that means two hours? Christ Almighty!” responded the cardinal, hastily crossing himself. “Why can’t we four – that’s me, the bishop, the local priest, and Friar Tuck – all pray together? Surely that would be quicker?”

“A revelation, your Eminence! May the merciful Lord forever shower bounteous blessings upon your Eminence.”

“Yes, yes, yes! So, how long would it take, wise guy?”

The chaplain fished out his iPhone, secreted in the unfathomable depths of the folds of his cassock and which he was only able to retrieve after removing his sash.

The battery was dead.

“Pardon me, your Eminence, but my phone needs charging. I don’t suppose…?”

The cardinal opened a drawer in his desk in which he kept a variety of electrical devices and cables. It was also where he kept a tablet (“how very Mosaic” he always thought when he used it) on which he was developing an app: *iConfess *was its working title.

“Lightning or thirty pin?”

A look of terror momentarily stole across the chaplain’s face, as if he were in mortal danger of being struck by the former or impaled on the latter, perhaps a twenty-first century version of the Iron Maiden.

“Your Eminence?”

“What sort of connector do you need?”

The phone now on charge, the cardinal repeated the question: “how much time do we need to block out in the diary to intercede for this doubly wretched actor if we all pray together?”

“Does your Eminence have a Bluetooth headset, by any chance?” “Oh, for heaven’s sake! Just get on with it!”

“Hey Siri!” yelled the chaplain in a voice which was loud enough to carry into the chapel at the far end of the quadrangle, interrupting the verger laying out the order of service for Vespers; “how long would it take to pray a soul out of purgatory who was twice as much in need of redemption as Kirk Douglas, if his Eminence only needs one hour, a bishop three hours, a priest five, and a friar seven for a common or garden sinner, but on this occasion they all pray together?”

The tinny answer came through. “On their own, the cardinal would need two hours, the bishop six, the priest ten and the friar fourteen; but because they are working in unison (“wishful thinking in today’s ecumenical environment,” thought the cardinal) we need to solve for x where x over 2, plus x over 6, plus x over 10, plus x over 14 equals 1. The common denominator of 2, 6, 10 and 14 is 420, so (for the cardinal) x over 2 times 420 means x equals 210. Applying the same calculation to the other participants, then x is 70 for the bishop, 42 for the priest, and 30 for the friar, resulting in a total value for x of 352. If 352 x equals 420, then x equals 420 divided by 352 which equals 1.19 roughly. So the intercession should take about one hour, eleven minutes and twenty-four seconds.”

“Halleluia!” exclaimed the cardinal. “That wasn’t difficult, was it?”

*You can find more entries from the Teddy Rocks Maths Competition here.*